/*! 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 33 Playing in the street, a child a... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 33

Playing in the street, a child accidentally tosses a ball at \(18 \mathrm{m} / \mathrm{s}\) toward the front of a car moving toward him at \(14 \mathrm{m} / \mathrm{s}\). What's the ball's speed after it rebounds elastically from the car?

Short Answer

Expert verified
The speed of the ball after it rebounds elastically from the car is \(18 m/s\).

Step by step solution

01

Understanding the Problem

The car and the ball are moving in opposite directions. Therefore, their relative speed is the sum of their individual speeds. We have the speed of the ball as \(18 m/s\) and the speed of the car as \(14 m/s\). So, their relative speed is \(18 m/s + 14 m/s = 32 m/s\).
02

Calculating the Ball鈥檚 Speed After Rebound

After the ball rebounds, it moves in the same direction as the car. However, since this is an elastic collision, the speed of the ball relative to the car remains the same. Therefore, the speed of the ball after its rebounds is the relative speed minus the speed of the car. Hence, \(32 m/s - 14 m/s = 18 m/s\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Relative Velocity
Relative velocity is an important concept when analyzing scenarios where two objects are moving in relation to each other, as it helps us understand their motion more clearly. The term "relative velocity" refers to the velocity of one object as observed from another moving object. In the original exercise, we deal with a ball moving towards a car. When calculating the relative velocity, we consider the speeds of both the ball and the car.

  • The ball moves at 18 m/s towards the car.
  • The car moves towards the ball at 14 m/s.
Together, since they move towards each other, their relative velocity is simply the sum of their speeds: 18 m/s + 14 m/s = 32 m/s. This means that as far as the ball is concerned, it is approaching the car at 32 m/s.
Conservation of Momentum
The conservation of momentum is another key principle when studying elastic collisions. It states that in an isolated system, the total momentum before and after a collision remains constant. This principle is grounded in Newton's laws of motion and is critical for solving collision-related problems.

In the provided homework exercise, while momentum itself is not directly calculated, the idea behind an elastic collision aligns with the conservation of momentum. In an elastic collision, kinetic energy is also conserved, meaning that there's no loss of energy in the system. The ball bounces off the car with the same speed it has in terms of relative velocity.

  • An elastic collision conserves both momentum and kinetic energy.
  • In this case, the ball reverses its direction while keeping its speed equal to the relative speed reduced by the car's speed.
  • This is why the speed of the ball remains at 18 m/s even after the rebound, moving in the direction of the car.
Rebounding Balls
Rebounding, especially in the context of balls, is a practical demonstration of elastic collisions. When a ball collides elastically with another object, it "bounces back" instead of sticking to the object. This bounce-back effect is attributed to how energy and momentum are transferred during the collision.

In elastic collisions like the one in this exercise, the ball returns with a speed that closely relates to its original speed, given the conservation laws we mentioned. The specific setup of the problem ensures that after colliding with the car, the ball rebounds with the same relative speed.

  • Bouncing or rebounding shows transfer and conservation of momentum and energy.
  • The ball keeps moving in the same speed (relative to its approach speed) due to the elastic nature of the collision.
  • For practical observation, a perfectly elastic rebound means no kinetic energy loss, although in real-world scenarios, some energy is usually transferred to heat or sound.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

\(\mathrm{A}^{238} \mathrm{U}\) nucleus is moving in the \(x\) -direction at \(5.0 \times 10^{5} \mathrm{m} / \mathrm{s}\) when it decays into an alpha particle \(\left(^{4} \mathrm{He}\right)\) and \(\mathrm{a}^{234} \mathrm{Th}\) nucleus. The alpha moves at \(1.4 \times 10^{7} \mathrm{m} / \mathrm{s}\) at \(22^{\circ}\) above the \(x\) -axis. Find the recoil velocity of the thorium.

Model rocket motors are specified by giving the impulse they "provide, in \(\mathrm{N} \cdot \mathrm{s}\), over the entire time the rocket is firing. The table below shows the results of rocket-motor tests with different motors used to launch rockets of different masses. Determine two data-based quantities that, when plotted against each other, should give a straight line and whose slope should allow you to determine \(g .\) Plot the data, establish a best-fit line, and determine \(g\). Assume that the maximum height is much greater than the distance over which the rocket motor is firing, so you can neglect the latter. You're also neglecting air resistance- -but explain how that affects your experimentally determined value for \(g\). $$\begin{array}{|l|r|r|r|r|r|} \hline \text { Impulse, } J(\mathrm{N} \cdot \mathrm{s}) & 4.5 & 7.8 & 4.5 & 7.8 & 11 \\ \hline \begin{array}{l}\text { Rocket mass }(\mathrm{g}) \\ \text { (including motor) }\end{array} & 180 & 485 & 234 & 234 & 485 \\ \hline \begin{array}{l}\text { Maximum height } \\\\\text { achieved (m) }\end{array} & 22 & 13 & 19 & 51 & 23 \\\\\hline\end{array}$$

How is it possible to have a collision between objects that don't ever touch? Give an example of such a collision.

An object with kinetic energy \(K\) explodes into two pieces, each of which moves with twice the speed of the original object. Find the ratio of the internal kinetic energy to the center-of-mass energy after the explosion.

An object collides elastically with an equal-mass object initially at rest. If the collision isn't head-on, show that the final velocity vectors are perpendicular.
See all solutions

Recommended explanations on Physics Textbooks

Mechanics and Materials

Read Explanation

Waves Physics

Read Explanation

Famous Physicists

Read Explanation

Circular Motion and Gravitation

Read Explanation

Magnetism

Read Explanation

Thermodynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.