Ch. 02 - Describing Motion: Kinematics in One Dimension

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook

Giancoli Douglas 5th edition

Ch. 02 - Describing Motion: Kinematics in One Dimension

Problem 100

Chapter 2, Problem 100

Bill can throw a ball vertically at a speed 1.5 times faster than Joe can. How many times higher will Bill's ball go than Joe's?

Verified step by step guidance

Identify the relationship between the maximum height of a projectile and its initial velocity. The maximum height (h) is given by the formula:

h = \frac{v^{2}}{2}

, where

v

is the initial velocity and

g

is the acceleration due to gravity.

Recognize that Bill's initial velocity is 1.5 times Joe's initial velocity. Let Joe's initial velocity be

v

_j, so Bill's initial velocity is

1.5 v

_j.

Substitute the initial velocities into the height formula for both Bill and Joe. For Joe:

h

_j=v_j22g. For Bill:

h

_b=1.5v_j22g.

Simplify the expression for Bill's height. Using

{1.5}^{2} = 2.25

, Bill's height becomes:

h

_b=2.25v_j22g.

Find the ratio of Bill's height to Joe's height:

h

_bh_j=2.251. This shows that Bill's ball will go 2.25 times higher than Joe's.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

12m

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinematics

Kinematics is the branch of mechanics that describes the motion of objects without considering the forces that cause the motion. It involves concepts such as displacement, velocity, and acceleration. In this context, understanding kinematics is essential to analyze how the initial speed of the ball affects its maximum height.

Projectile Motion

Projectile motion refers to the motion of an object that is thrown or projected into the air, subject only to the acceleration of gravity. For vertical throws, the maximum height reached by the projectile can be calculated using the initial velocity and the acceleration due to gravity. This concept is crucial for determining how the height of Bill's throw compares to Joe's.

Energy Conservation

The principle of energy conservation states that energy cannot be created or destroyed, only transformed from one form to another. In the context of projectile motion, the kinetic energy of the ball at the moment of release is converted into gravitational potential energy at its peak height. This relationship helps in calculating the heights reached by Bill and Joe based on their respective throwing speeds.

Recommended video:

Guided course

06:24

Conservation Of Mechanical Energy

Related Practice

Textbook Question

A robot used in a pharmacy picks up a medicine bottle at t = 0. It accelerates at 0.20 m/s² for 4.5 s, then travels without acceleration for 68 s and finally decelerates at ―0.40 m/s² for 2.5 s to reach the counter where the pharmacist will take the medicine from the robot. From how far away did the robot fetch the medicine?

views

Textbook Question

Figure 2–55 shows the position vs. time graph for two bicycles, A and B. At which instant(s) are the bicycles passing each other? Which bicycle is passing the other?

views

Textbook Question

A parachutist bails out of an airplane, and freely falls 75 m (ignore air friction). Then the parachute opens, and her acceleration is ― 1.5 m/s² (up). The parachutist reaches the ground with a speed of 1.5 m/s. From how high did she bail out of the plane?

views

Textbook Question

Suppose a 65-kg person jumps from a height of 3.0 m down to the ground. What is the speed of the person just before landing (Chapter 2)?

<IMAGE>

views

Textbook Question

Figure 2–55 shows the position vs. time graph for two bicycles, A and B. Which bicycle has the larger average velocity?

views