/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 The velocity of a ball thrown st... [FREE SOLUTION] | 91Ó°ÊÓ

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The velocity of a ball thrown straight up decreases as it rises. Does its acceleration increase, decrease, or remain the same as the ball rises? Explain your answer.

Short Answer

Expert verified
The acceleration of the ball remains the same as it rises. This is because acceleration in this context is due to gravity, which is a constant force.

Step by step solution

01

Understanding the Terms

Firstly, understand the definitions of velocity and acceleration. Velocity is the rate at which an object changes its position, i.e., speed in a given direction. Acceleration, on the other hand, is the rate of change of velocity.
02

Considering the Effect of Gravity

When a ball is thrown upward, it initially has a high velocity that decreases as the ball rises due to the force of gravity. Gravity is a force that pulls objects towards the earth. Therefore, it will slow down the upwards movement of the ball, reducing its velocity.
03

Determining the Acceleration

The gravity 'pulling' the ball down is an acceleration. Through the journey of the ball, gravity remains constant. Although the velocity is decreasing, the acceleration due to gravity is constant. It doesn't increase or decrease during the ball's upward travel but remains constant. In fact, this acceleration is acting against the ball's rise, causing the decrease in velocity.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Velocity
Velocity refers to the speed of an object moving in a particular direction. When throwing a ball straight up, its velocity initially is quite high as it's propelled away from your hand.
However, as the ball ascends, its speed decreases. This happens because the force of gravity pulls it back towards the earth.
Imagine the ball is like a car going uphill; it's struggling somewhat because there's a consistent backward force acting on it, which in this case, is gravity.

Even though the velocity decreases as the ball goes up, velocity itself is a vector quantity. This means that both the speed and the direction of the ball are involved in determining the velocity.
As soon as the ball reaches the peak of its height, the velocity becomes zero for a moment before it starts coming down.
  • This change in velocity shows that motion is happening in a straight line directed upwards and then downwards through the air.
  • Understanding velocity helps us know how quickly something is moving and in which direction.
Acceleration
Acceleration is an important concept in physics that involves a change in the velocity of an object over time. It's helpful to think of acceleration as the car's gas pedal, but in physics!
For a ball thrown up in the air, the acceleration occurs due to gravity.

Even as the ball's velocity decreases while rising, its acceleration remains unaffected, always pointing downward. This constant downward acceleration is the result of gravity acting on the ball.
Regardless of how hard you initially throw the ball, gravity's effect doesn't change its acceleration; it's a constant.

In the case of upward motion, this acceleration results in a deceleration or a reduction of upward speed.
  • When the ball moves up, gravity still pulls it downwards, showing up as a negative acceleration to the upwards velocity.
  • This consistent movement driven by the unchanging force of gravity provides a perfect example of constant acceleration in nature.
Gravity
Gravity is the force that pulls objects toward the center of the Earth. It's a literal game changer, making things that go up, come back down.
Consider gravity as an unseen hand that pulls the ball back down once thrown upward.

In projectile motion, gravity is a consistent force and plays a crucial role in determining the trajectory (or path) of the moving object.
This constant force doesn't vary with the direction or speed of the ball's movement.
  • Gravity always acts downwards at approximately 9.8 meters per second squared (m/s²), affecting the ball the same at all heights.
  • This constant downward pull is why after reaching the maximum height, the ball will begin to descend back down to the ground.
Understanding gravity's role is essential for grasping not only projectile motion but all kinds of motion on Earth and beyond.

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Most popular questions from this chapter

A car traveling \(80 \mathrm{~km} / \mathrm{h}\) is \(1500 \mathrm{~m}\) behind a truck traveling at \(70 \mathrm{~km} / \mathrm{h}\). How long will it take the car to reach the truck?

Mary spots Bill approaching the dorm at a constant rate of \(2 \mathrm{~m} / \mathrm{s}\) on the walkway that passes directly beneath her window, \(17 \mathrm{~m}\) above the ground. When Bill is \(120 \mathrm{~m}\) away from the point below her window she decided to drop an apple down to him. (See Figure 2-26.) (a) How long should Mary wait to drop the apple if Bill is to catch it \(1.75 \mathrm{~m}\) above the ground, and without either speeding up or slowing down? (b) How far from directly below the window is Bill when Mary releases the apple? (c) What is the angle between the vertical and the line of sight between Mary and Bill at the instant Mary releases the apple? Ignore the effects of air resistance. SSM

•A two-stage rocket blasts off vertically from rest on a launchpad. During the first stage, which lasts for \(15.0 \mathrm{~s}\), the acceleration is a constant \(2.00 \mathrm{~m} / \mathrm{s}^{2}\) upward. After \(15.0 \mathrm{~s}\), the first engine stops and the second stage engine fires, producing an upward acceleration of \(3.00 \mathrm{~m} / \mathrm{s}^{2}\) that lasts for \(12.0 \mathrm{~s}\). At the end of the second stage, the engines no longer fire and therefore cause no acceleration, so the rocket coasts to its maximum altitude. (a) What is the maximum altitude of the rocket? (b) Over the time interval from blastoff at the launchpad to the instant that the rocket falls back to the launchpad, what are its (i) average speed and (ii) average velocity? Ignore the effects of air resistance.

. • Calc A lizard is running in a straight line according to the following: \(x(t)=\left(0.20 \mathrm{~m} / \mathrm{s}^{3}\right) t^{3}-\left(0.40 \mathrm{~m} / \mathrm{s}^{2}\right) t^{2}-(0.65 \mathrm{~m} / \mathrm{s}) t\) (a) Determine \(v(t)\). (b) Calculate the velocity when \(t=2 \mathrm{~s}\), \(t=4 \mathrm{~s}\), and \(t=10 \mathrm{~s}\). (c) When is the lizard at rest? (d) When is the lizard moving in the positive \(x\) direction? (e) When is the lizard moving in the negative \(x\) direction? (f) When does the lizard have zero acceleration? (g) What distance does the lizard travel (not its displacement) in the first \(10 \mathrm{~s}\) ?

A runner starts from rest and achieves a maximum speed of \(8.97 \mathrm{~m} / \mathrm{s}\). If her acceleration is \(9.77 \mathrm{~m} / \mathrm{s}^{2}\), how long will it take her to reach that speed? SSM

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