A Car Starts from rest and accelerate at the rate of
5m/s' for 8 See It then travels at this speed for another lasse
fer which it was brought to rest in 4sec:
The maximum velocity attained by the car
the time taken to cover the first 18seconds
Calculate the average speed of the Car

Answer:

Explanation:

The answer is **(c) 9.39 m/s** for the velocity of the bullet-block system after it's hit, and **(g) 209.39 m/s** for the bullet's velocity before it hit the box.

The velocity of the bullet-block system after it's hit can be found using the conservation of energy. The potential energy of the box before it was hit is mgh, where m is the mass of the box, g is the acceleration due to gravity, and h is the height that the box was displaced. After the bullet hits the box, the potential energy of the box is zero, but the kinetic energy of the bullet-block system is mv^2/2, where m is the total mass of the bullet-block system and v is the velocity of the bullet-block system. Setting these two expressions equal to each other, we get:

```

mgh = mv^2/2

```

Solving for v, we get:

```

v = sqrt(2mgh)

```

In this case, we have:

* m = 0.05 kg + 1.3 kg = 1.35 kg

* g = 9.8 m/s^2

* h = 4.5 m

So, the velocity of the bullet-block system after it's hit is:

```

v = sqrt(2 * 1.35 kg * 9.8 m/s^2 * 4.5 m) = 9.39 m/s

```

The velocity of the bullet before it hit the box can be found using the conservation of momentum. The momentum of the bullet before it hit the box is mv, where m is the mass of the bullet and v is the velocity of the bullet. After the bullet hits the box, the momentum of the bullet-block system is (m + M)v, where M is the mass of the box and v is the velocity of the bullet-block system. Setting these two expressions equal to each other, we get:

```

mv = (m + M)v

```

Solving for v, we get:

```

v = mv/(m + M)

```

In this case, we have:

* m = 0.05 kg

* M = 1.3 kg

* v = 9.39 m/s

So, the velocity of the bullet before it hit the box is:

```

v = 0.05 kg * 9.39 m/s / (0.05 kg + 1.3 kg) = 209.39 m/s

```

The velocity of the bullet-block system after the collision is approximately a) 6.76 m/s, and the bullet's velocity before it hit the box is approximately e) 196.76 m/s.

To solve this problem, we can apply the principle of conservation of momentum and the principle of conservation of mechanical energy.

First, let's calculate the velocity of the bullet-block system after the collision. We can use the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision.

Let m1 be the mass of the bullet (0.05 kg) and m2 be the mass of the box (1.3 kg). Let v1 be the velocity of the bullet before the collision (which we need to find) and v2 be the velocity of the bullet-block system after the collision.

Using the conservation of momentum:

m1 * v1 = (m1 + m2) * v2

0.05 kg * v1 = (0.05 kg + 1.3 kg) * v2

0.05 kg * v1 = 1.35 kg * v2

Now, let's calculate the velocity of the bullet-block system (v2). Since the system goes up by a height of 4.5 m, we can use the principle of conservation of mechanical energy.

m1 * v1^2 = (m1 + m2) * v2^2 + m2 * g * h

0.05 kg * v1^2 = 1.35 kg * v2^2 + 1.3 kg * 9.8 m/s^2 * 4.5 m

Now, we can substitute the value of v2 from the momentum equation into the energy equation and solve for v1.

By solving these equations, we find that v1 is approximately 196.76 m/s.

Therefore, the bullet's velocity before it hit the box is approximately 196.76 m/s. (e) 196.76 m/s

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Answer:

Refer to the step-by-step Explanation.

Step-by-step Explanation:

Simplify the equation with given substitutions,

Given Equation:

\(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2\)

Given Substitutions:

\(\omega=v/R\\\\ \omega_{_{0}}=v_{_{0}}/R\\\\\ I=(2/5)mR^2\)\(\hrulefill\)

Start by substituting in the appropriate values: \(mgh+(1/2)mv^2+(1/2)I \omega^2=(1/2)mv_{_{0}}^2+(1/2)I \omega_{_{0}}^2 \\\\\\\\\Longrightarrow mgh+(1/2)mv^2+(1/2)\bold{[(2/5)mR^2]} \bold{[v/R]}^2=(1/2)mv_{_{0}}^2+(1/2)\bold{[(2/5)mR^2]}\bold{[v_{_{0}}/R]}^2\)

Adjusting the equation so it easier to work with.\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the left-hand side of the equation:

\(mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

Simplifying the third term.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2} \Big[\dfrac{2}{5} mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{2}\cdot \dfrac{2}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v}{R} \Big]^2\)

\(\\ \boxed{\left\begin{array}{ccc}\text{\Underline{Power of a Fraction Rule:}}\\\\\Big(\dfrac{a}{b}\Big)^2=\dfrac{a^2}{b^2} \end{array}\right }\)

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2 \cdot\dfrac{v^2}{R^2} \Big]\)

"R²'s" cancel, we are left with:

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5}mv^2\)

We have like terms, combine them.

\(\Longrightarrow mgh+\dfrac{1}{2} mv^2+\dfrac{1}{5} \Big[mR^2\Big]\Big[\dfrac{v^2}{R^2} \Big]\\\\\\\\\Longrightarrow mgh+\dfrac{7}{10} mv^2\)

Each term has an "m" in common, factor it out.

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)\)

Now we have the following equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac12mv_{_{0}}^2+\dfrac12\Big[\dfrac25mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\)

\(\hrulefill\)

Simplifying the right-hand side of the equation:

\(\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac12\cdot\dfrac25\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}}{R}\Big]^2\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\Big]\Big[\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15\Big[mR^2\cdot\dfrac{v_{_{0}}^2}{R^2}\Big]\\\\\\\\\Longrightarrow \dfrac12mv_{_{0}}^2+\dfrac15mv_{_{0}}^2\Big\\\\\\\\\)

\(\Longrightarrow \dfrac{7}{10}mv_{_{0}}^2\)

Now we have the equation:

\(\Longrightarrow m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

\(\hrulefill\)

Now solving the equation for the variable "v":

\(m(gh+\dfrac{7}{10}v^2)=\dfrac{7}{10}mv_{_{0}}^2\)

Dividing each side by "m," this will cancel the "m" variable on each side.

\(\Longrightarrow gh+\dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2\)

Subtract the term "gh" from either side of the equation.

\(\Longrightarrow \dfrac{7}{10}v^2=\dfrac{7}{10}v_{_{0}}^2-gh\)

Multiply each side of the equation by "10/7."

\(\Longrightarrow v^2=\dfrac{10}{7}\cdot\dfrac{7}{10}v_{_{0}}^2-\dfrac{10}{7}gh\\\\\\\\\Longrightarrow v^2=v_{_{0}}^2-\dfrac{10}{7}gh\)

Now squaring both sides.

\(\Longrightarrow \boxed{\boxed{v=\sqrt{v_{_{0}}^2-\dfrac{10}{7}gh}}}\)

Thus, the simplified equation above matches the simplified equation that was given.  

A. The average speed you can use to pull the safe is 1.02 m/s

B. The time needed to pull the safe up is 17.65 s

First, we shall obtain the force. This is shown below:

F = mg

F = 60 × 9.8

F = 588 N

Finally, we shall obtain the average speed. Details below:

Power = force × average speed

600 = 588 × average speed

Divide both sides by 588

Average speed = 600 / 588

Average speed = 1.02 m/s

The time needed to pull the safe up can be obtained as follow:

Time = Total distance / average speed

Time = 18 / 1.02

Time = 17.65 s

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Complete question:

You know you can provide 600 W

of power to move large objects. You need to move a 60-kg

safe up to a storage loft, 18 m

above the floor.

Part A

With what average speed can you pull the safe straight up?

Part B

What is the time needed to pull the safe up?

Answer:

That people are motivated by a series of five universal needs.

Explanation:

The dragonfly must generate approximately 4.8 × 10^-4 Joules of energy to spin itself at a rate of 1100 rpm.

Start by converting the rotational speed from rpm (revolutions per minute) to rad/s (radians per second). Since 1 revolution is equal to 2π radians, we can use the conversion factor:

Angular speed (ω) = (1100 rpm) × (2π rad/1 min) × (1 min/60 s)

ω ≈ 115.28 rad/s

The moment of inertia (I) is given as 2.0 × 10^-7 kg⋅m².

Use the formula for rotational kinetic energy:

Rotational Kinetic Energy (KE_rot) = (1/2) I ω²

Substituting the given values:

KE_rot = (1/2) × (2.0 × 10^-7 kg⋅m²) × (115.28 rad/s)²

Calculate the value inside the parentheses:

KE_rot ≈ (1/2) × (2.0 × 10^-7 kg⋅m²) × (13274.28 rad²/s²)

KE_rot ≈ 1.331 × 10^-3 J

Round the result to the proper number of significant figures, which in this case is three, as indicated by the given moment of inertia.

KE_rot ≈ 4.8 × 10^-4 J

Therefore, the dragonfly must generate approximately 4.8 × 10^-4 Joules of energy to spin itself at a rate of 1100 rpm.

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If the metal ion has a 3+ charge and the nonmetal ion has a 4- charge, the formula of the compound is X4Z3.

The formula of an ionic compound is determined by the charges of the ions that make up the compound. Recall that when the compound is  formed, the ions exchange valences.

Hence, is the metal ion has a 3+ charge and the nonmetal ion has a 4- charge, the formula of the compound is X4Z3.

Missing parts:

A metal ion (X) with a charge of 3+ is attracted to a nonmetal ion (Z) with a charge of 4-. Which of these formulas represents the resulting compound.

A. 7XZ

B. X3Z4

C. X4Z3

D. 4X3Z

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Answer:

As the load increases the motor generally reduces rpm, as the happens the counter emf generated in the armature decreases, causing more current to flow to

Explanation:

Answer:

143.2 m

Explanation:

Final speed is 0, initial speed is 29.8 m/s, a = -3.1 m/s²

v² = v₀² + 2aΔx

0 = (29.8 m/s)² + 2(-3.1 m/s²)(Δx)

Δx = -(29.8 m/s)² / 2(-3.1 m/s²) = -888 m²/s² / -6.2 m/s² = 143.2 m

Answer:

Explanation:Force and acceleration are directly proportional. ... Mass and acceleration are inversely proportional. In this situation, acceleration changes in response to a change of mass, so mass is the independent variable and acceleration is the dependent variable.

a) The takeoff speed of the froghopper can be found using the following equation:

v^2 = 2gh/(1 - cos^2(theta))

where:

v = takeoff speed

g = acceleration due to gravity (9.81 m/s^2)

h = maximum height (293 mm = 0.293 m)

theta = takeoff angle (62.0 degrees)

Substituting the given values into the equation, we get:

v^2 = 2(9.81)(0.293)/(1 - cos^2(62.0))

v^2 = 0.571

v = sqrt(0.571)

v ≈ 0.756 m/s

Therefore, the takeoff speed of the froghopper is approximately 0.756 m/s.

b) The kinetic energy generated by the froghopper can be found using the following equation:

KE = 0.5mv^2

where:

m = mass (12.8 mg = 0.0128 g)

v = takeoff speed (0.756 m/s)

Substituting the given values into the equation, we get:

KE = 0.5(0.0128)(0.756)^2

KE ≈ 0.00346 J

(1 J = 10^6 microjoules)

Therefore, the kinetic energy generated by the froghopper for this jump is approximately 0.00346 microjoules.

c) The energy per unit body mass required for this jump can be found by dividing the kinetic energy by the mass of the froghopper:

energy per unit body mass = KE/m

Substituting the values we obtained earlier, we get:

energy per unit body mass = 0.00346/0.0128

energy per unit body mass ≈ 0.270 J/kg

Therefore, the energy per unit body mass required for this jump is approximately 0.270 joules per kilogram of body mass.

Answer:

All points to the left of zero are negative

Explanation:

Answer:

C

Explanation:

on edge

1. People have to prepare for natural disasters in order to reduce the risk of injury, death, and property damage caused by the disaster.

Natural disasters are adverse events that occur naturally and are a result of the interaction between the physical environment and human activities. They can include floods, hurricanes, tornadoes, earthquakes, tsunamis, wildfires, landslides, volcanic eruptions, and extreme weather events. Natural disasters can have devastating impacts on communities, including loss of life, damage to property, displacement, and destruction of livelihoods. Governments, organizations, and individuals are increasingly working to reduce the impacts of natural disasters through improved risk management, infrastructure planning, and disaster response and recovery efforts.

2. People have to prepare for natural disasters in order to be able to respond quickly and efficiently in the event of an emergency.

3. People have to prepare for natural disasters in order to plan for the financial impacts of the disaster.

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To perform a drug lookup to ensure that the new compound has been added to the computer system properly we have to select the new from the toolbar at the top of the screen

A computer system is a collection of computers, related hardware, and related software. The central processing unit (CPU), memory, input/output, and storage devices are the four main components of a computer system. To produce the desired result, all of these parts operate in concert as a single unit.

Selecting the new from the toolbar at the top of the screen will allow us to run a drug lookup to make sure the new compound has been properly added to the computer system.

Therefore the correct answer is the option C

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Answer:

africa

Explanation:

África África ooo

Answer:

Positive reinforcement

Answer:

If two bumper cars collide with a certain force, then they will move away from each other in opposite directions with the same force. This demonstrates Newton's third law, which states that for every action, there is an equal and opposite reaction.

Explanation:

The Big Bang theory is the most widely accepted explanation for the origins of the universe, but it does not necessarily imply that the universe emerged from nothing.

It is possible that new discoveries or insights may shed light on this fundamental question in the future. The universe may have arisen from a pre-existing state or through some other natural process that we do not yet understand.

Instead, the theory describes how the universe underwent a rapid expansion from a very dense and hot state. The conditions and laws of physics that applied during the earliest moments of the universe may not necessarily be the same as those we observe today, and there are many unknowns and uncertainties in our understanding of these early stages.

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Answer:

using sand

Explanation:

We can increase friction by making rough surface.

The weight of cart can be expressed as,

Plug in the known value,

The work done on the cart can be expressed as,

According to work energy theorem,

Since the cart is initially at rest therefore, initial speed of cart is zero. Plug in the known expression,

Substitute the known values,

Thus, the final velocity of cart is 140 m/s.

The most appropriate method to study the potential impacts of oil drilling on coastal California would be design a computer simulation of an oil spill in the area to determine the environmental impact design a computer simulation of an oil spill in the area to determine the environmental impact. The correct option to this question is C.

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The correct statement is " A dry cell battery has magnetic properties.", The correct option is C.

A dry cell battery does generate its own magnetic field due to the flow of electric current through the battery.

The magnetic field is created by the movement of charged particles (electrons) within the battery. This magnetic field is relatively weak and is not typically strong enough to be used for practical applications outside of the battery itself.

So, the magnetic properties of the dry cell battery are important for understanding its behavior within an electrical circuit.

Therefore, The correct answer is option C.

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All the objects are motionless, so kinetic energy of each object is zero after the collision.

The kinetic energy of an object is defined as the energy which is  possesses due to its motion. It is the work required to accelerate a body of a given mass from rest to its stated velocity. This energy is gained during its acceleration, the body maintains the kinetic energy as long as its momentum does not change.

Kinetic Energy can be expressed as

\(K.E.=\) \(1/2 mv^2\)

Where, m is the mass of the object

v is the velocity.

It is expressed in joules (J).

After the collision all the objects are at rest, therefore, the final kinetic energy is also zero which shows maximum loss of kinetic energy. Such collisions are called perfectly inelastic.

Thus, all the objects are motionless, so kinetic energy of each object is zero after the collision.

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Answer:

920000

Explanation:

Each kg contains 1,000 grams

Complete Question

A radio technician measures the frequency of an AM radio transmitter. The frequency is 14603 kHz . What is the frequency in megahertz? Write your answer as a decimal.

Answer:

The value is  \(x = 14.6 \ MHz\)

Explanation:

From the question we are told that

  The  frequency is  \(f = 14603 \ kHz = 14603 *1000 = 14603000 \ Hz\)

Generally  

       \(1 Hz \to 1.0 *10^{-6} \ MHz\)

       \(14603000 \ Hz \to x MHz\)

=>   \(x = \frac{14603000 * 1.0*10^{-6}}{1 }\)

=>    \(x = 14.6 \ MHz\)

Option C. The heat absorbed or lost by a substance while it's changing state  correctly describes latent heat

Latent heat is the heat absorbed or lost by a substance while it is changing state.

The latent heat is a type of heat that is transferred during phase change, i.e., while a substance undergoes a change of state.

For example, when ice melts into liquid water, or when liquid water evaporates into water vapor, heat is absorbed from the surroundings.

Latent heat is not associated with a temperature change; rather, it's associated with a change of state.

For instance, the temperature of water remains at 100°C while boiling.

When water is boiling, the latent heat of vaporization is absorbed and utilized to break the hydrogen bonds holding water molecules together to change water from the liquid phase to the gaseous phase.

When the water is boiling, adding more heat won't increase the water's temperature, instead, the extra heat will be absorbed to change the phase of water molecules.

Therefore, the correct answer to the given question is option C: The heat absorbed or lost by a substance while it is changing state.

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Two forces f1=(8i+3j)N and f2=(4i+6j) are acting on 5kg object then  the magnitude of the resultant force is 15 N and the direction of the resultant force is approximately 36.87 degrees from the positive x-axis.

The acceleration of the object in the x-component (\(a_x\)) is 2.4  \(m/s^{2}\), and the acceleration in the y-component (\(a_y\)) is 1.8  \(m/s^{2}\).

The magnitude of the acceleration of the object is 3  \(m/s^{2}\).

To find the magnitude and direction of the resultant force, we need to add the two given forces together.

Given:

f1 = (8i + 3j) N

f2 = (4i + 6j) N

To find the resultant force (\(F_res\)), we simply add the corresponding components:

\(F_res\) = f1 + f2

= (8i + 3j) + (4i + 6j)

= (8 + 4)i + (3 + 6)j

= 12i + 9j

The magnitude of the resultant force (\(|F_res|\)) can be found using the Pythagorean theorem:

\(|F_res|\)= \(\sqrt{(12^2) + (9^2)}\)

= \(\sqrt{144 + 81}\)

= \(\sqrt{225}\)

= 15 N

So, the magnitude of the resultant force is 15 N.

To find the direction of the resultant force, we can use trigonometry. The direction can be represented by the angle θ between the positive x-axis and the resultant force vector. We can calculate θ using the inverse tangent function:

θ = arctan(9/12)

= arctan(3/4)

≈ 36.87 degrees

Therefore, the direction of the resultant force is approximately 36.87 degrees from the positive x-axis.

Now let's calculate the acceleration of the object in the x and y components. We know that force (F) is related to acceleration (a) through Newton's second law:

F = ma

For the x-component:

\(F_x\)= 12 N

m = 5 kg

Using  \(F_x\)= \(ma_x\), we can solve for \(a_x\):

12 N = 5 kg * \(a_x\)

\(a_x\)= 12 N / 5 kg

\(a_x\) = 2.4 \(m/s^{2}\)

For the y-component:

\(F_y\) = 9 N

m = 5 kg

Using \(F_y\) = \(ma_y\), we can solve for \(a_y\):

9 N = 5 kg * \(a_y\)

\(a_y\) = 9 N / 5 kg

\(a_y\)= 1.8  \(m/s^{2}\)

So, the acceleration of the object in the x-component (\(a_x\)) is 2.4  \(m/s^{2}\), and the acceleration in the y-component (\(a_y\)) is 1.8  \(m/s^{2}\).

To find the magnitude of the acceleration (|a|), we can use the Pythagorean theorem:

|a| = \(\sqrt{(a_x^2) + (a_y^2)}\)

= \(\sqrt{(2.4^2) + (1.8^2}\)

= \(\sqrt{5.76 + 3.24}\)

= \(\sqrt{9}\)

= 3  \(m/s^{2}\)

Therefore, the magnitude of the acceleration of the object is 3  \(m/s^{2}\)

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The amount the needle on the meter is deflected A. increases

This phenomenon can be explained by Faraday's law of electromagnetic induction. According to this law, when a magnetic field (created by the bar magnet) passes through a coil of wire, it induces an electric current in the wire. This induced current generates its own magnetic field, which interacts with the magnetic field of the bar magnet.

The deflection of the meter needle is a result of this induced current. When the number of coils of wire is increased, there is a greater number of wire loops for the magnetic field to pass through. This leads to a stronger induction of electric current, resulting in a larger deflection of the meter needle.

By increasing the number of coils, more magnetic flux is linked with the wire, resulting in a higher induced electromotive force (emf) and a greater current. This increased current produces a stronger magnetic field around the wire, leading to a larger deflection on the meter. Therefore, increasing the number of coils of wire enhances the magnetic field interaction, resulting in an increased deflection of the meter needle. Therefore, Option A is correct.

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1. Diagram and Variables:

                                   Maximum Height

                                          |

                                          |

                                          |

                                          |

                                          |

                                          |

                                          |

                                          |

                                          |

------------------------ Ground ------------------------>

Variables:

Initial velocity (v₀) = 90 m/s

Launch angle (θ) = 45°

Maximum height (H)

Time of travel at maximum height (t_max_height)

Horizontal displacement at maximum height (d_max_height)

Time of travel at maximum range (t_max_range)

Horizontal displacement at maximum range (d_max_range)

2. For when the round reaches maximum height:

a) Time of travel (t_max_height):

At the maximum height, the vertical velocity (v_y) becomes zero. To find the time it takes for the round to reach the maximum height, we can use the equation for vertical motion:

v_y = v₀ * sin(θ) - g * t

0 = v₀ * sin(θ) - g * t_max_height

Solving for t_max_height:

t_max_height = v₀ * sin(θ) / g

Substituting the values:

t_max_height = 90 m/s * sin(45°) / 9.8 m/s²

Calculating the value:

t_max_height ≈ 6.12 s

b) Horizontal displacement (d_max_height):

The horizontal displacement at maximum height can be calculated using the equation:

d_max_height = v₀ * cos(θ) * t_max_height

Substituting the values:

d_max_height = 90 m/s * cos(45°) * 6.12 s

Calculating the value:

d_max_height ≈ 385.94 m

Therefore, at the maximum height, the time of travel is approximately 6.12 seconds, and the horizontal displacement is approximately 385.94 meters.

3. For when the round reaches maximum range:

a) Time of travel (t_max_range):

To find the time it takes for the round to reach the maximum range, we can consider the symmetry of projectile motion. The time of flight (t_flight) is twice the time it takes to reach maximum height:

t_flight = 2 * t_max_height

Substituting the value of t_max_height:

t_max_range = 2 * 6.12 s

Calculating the value:

t_max_range ≈ 12.24 s

b) Horizontal displacement (d_max_range):

The horizontal displacement at maximum range can be calculated using the equation:

d_max_range = v₀ * cos(θ) * t_max_range

Substituting the values:

d_max_range = 90 m/s * cos(45°) * 12.24 s

Calculating the value:

d_max_range ≈ 868.63 m

Therefore, at the maximum range, the time of travel is approximately 12.24 seconds, and the horizontal displacement is approximately 868.63 meters.

When a mortar is fired at an angle of 45 degrees, it will reach its maximum height in 6.49 seconds and its maximum range in 12.98 seconds. The horizontal displacement of the mortar when it reaches its maximum height will be 413.02 meters, and its horizontal displacement when it reaches its maximum range will be 826.53 meters.

1. To draw a diagram of the described scenario, you can start by drawing a coordinate system. The x-axis represents the horizontal direction, and the y-axis represents the vertical direction. Place the origin (0, 0) at the point of launch. Since the mortar is angled 45 degrees from the horizontal, you can draw a line representing the initial direction of the round at a 45-degree angle from the x-axis.

Next, label the variables along the x and y dimensions. For the x-dimension, you can label the variable as "horizontal displacement" or simply "x." For the y-dimension, you can label the variable as "vertical displacement" or "height" and indicate that it is measured in meters.

2. When the round reaches maximum height:

a)

The time of ascent  can be calculated using the following formula:

time = ( initial velocity * sin(angle)) / acceleration due to gravity

In this case, the initial velocity is 90 meters per second, and the angle is 45 degrees. The acceleration due to gravity is typically considered to be approximately 9.8 meters per second squared.

Plugging in the values:

time = (90 * sin(45)) / 9.8  = 6.49s

b) The horizontal displacement at maximum height is :

horizontal displacement = initial velocity * cos (45) * time of ascent

Plugging in the values:

horizontal displacement=90* cos (45) * 6.49s= 413.02m

3. When the round reaches maximum range:

a) The time of travel can be calculated using the following formula:

time = (2 * initial velocity * sin(angle)) / acceleration due to gravity

The initial velocity and angle remain the same.

Plugging in the values:

time = (2 * 90 * sin(45)) / 9.8= 12.98s

b) The horizontal displacement at maximum range can be calculated using the following formula:

horizontal displacement = (initial velocity^2 * sin(2*angle)) / acceleration due to gravity

Plugging in the values:

horizontal displacement = (90^2 * sin(2*45)) / 9.8= 826.53m

Therefore, A mortar will reach its maximum height and distance when shot at a 45-degree angle in 6.49 and 12.98 seconds, respectively. When the mortar achieves its maximum height, its horizontal displacement will be 413.02 meters, and when it reaches its maximum range, it will be 826.53 meters.

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One of the conclusion about the history of sports that can be drawn from the movie "Champions" is that sports have a long and rich history that is intertwined with the history of human civilization.

From the ancient Olympic Games to the modern-day Olympics, sports have been a way for people to come together and compete in a spirit of sportsmanship and competition. Sports have also been a way for people to express themselves, to build community, and to achieve personal goals.

The movie "Champions" tells the story of a group of young men who come together to form a football team. The team is made up of boys from different backgrounds and with different abilities. However, they are all united by their love of football and their desire to win.

Find out more on history of the sports here: https://brainly.com/question/20843217

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