Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Book Icon
Chapter 3, Problem 94P

(a)

To determine

The distance of the ball strikes the wall.

(a)

Expert Solution
Check Mark

Answer to Problem 94P

The distance of the ball strikes the wall is 1.1m.

Explanation of Solution

Write the equation of motion for the ball taken to reach the wall.

Δx=vxΔt (I)

Here, Δx is the displacement of the ball, vx is the velocity of the ball along x axis, and Δt is the time taken by the ball to reach the wall.

Write the equation of motion for the ball’s initial velocity along x axis.

vx=vicosθ (II)

Here, vi is the initial velocity of the ball and θ is the vertical angle above the ground.

Write the equation of motion for the ball’s initial velocity along y axis.

viy=visinθ (III)

Here, vi is the initial velocity of the ball and θ is the vertical angle above the ground.

Write the equation of motion for the ball reaches certain height.

Δy=viyΔt+12ayΔt2

Here, Δy is the change in height of the ball, viy is the initial velocity of the ball along y axis, and ay is the acceleration of the ball.

Rewrite the above equation for gravitational acceleration.

Δy=viyΔt12gΔt2 (IV)

Here, g is the gravitational acceleration.

Write the equation for change in height of the ball.

Δy=yfyi (V)

Here, yf is the final height and yi is the initial height.

Conclusion:

Substitute equation (II) in equation (I) to find Δt.

Δx=(vicosθ)ΔtΔt=Δxvicosθ (VI)

Substitute equation (III) and (VI) in equation (IV) to find Δy.

Δy=(visinθ)Δt12gΔt2=(visinθ)Δxvicosθ12g(Δx2vi2cos2θ)=Δxtanθ(gΔx22vi2cos2θ)

Substitute the above relation in equation (V) to find yf.

yf=yi+Δy=yi+Δxtanθ(gΔx22vi2cos2θ)

Substitute 60cm for yi, 10m for Δx, 9.80m/s2 for g, 20m/s for vi, and 90°80°=10° for θ in the above equation.

yf=60cm(0.01m1cm)+(10m)tan10°((9.80m/s2)(10m)22(20m/s)2cos210°)=2.36m980m3/s2775.9m2/s2=2.36m1.26m=1.1m

Therefore, the distance of the ball strikes the wall is 1.1m.

(b)

To determine

Whether the ball rolls up or down when it hits the wall.

(b)

Expert Solution
Check Mark

Answer to Problem 94P

The ball rolls down when it hits the wall.

Explanation of Solution

Write the equation for change in velocity of the ball along y axis.

Δv=vfyviy (VII)

Here, vfy is the final velocity and viy is the initial velocity.

Write the equation of motion for the acceleration of ball.

Δv=ayΔt (VIII)

Here, Δv is the change in velocity.

Rewrite the equation (VIII) for gravitational acceleration.

Δv=gΔt (IX)

Conclusion:

Compare equation (VII) and (IX).

vfyviy=gΔt

Replace visinθ for viy and Δxvicosθ for Δt in above relation.

vfyvisinθ=g(Δxvicosθ)vfy=visinθ(gΔxvicosθ) (X)

Substitute 10m for Δx, 9.80m/s2 for g, 20m/s for vi, and 90°80°=10° for θ in equation (X).

vfy=(20m/s)sin10°((9.80m/s2)(10m)(20m/s)cos10°)=3.47m/s4.98m/s=1.51m/s1.5m/s

Since,vfy<0, so that ball is on its way down.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 3 Solutions

Physics

Ch. 3.5 - Prob. 3.6PPCh. 3.5 - Prob. 3.5ACPCh. 3.5 - Prob. 3.7PPCh. 3.5 - Prob. 3.5BCPCh. 3.5 - Prob. 3.8PPCh. 3.6 - Prob. 3.6CPCh. 3.6 - Prob. 3.9PPCh. 3.6 - Prob. 3.10PPCh. 3 - Prob. 1CQCh. 3 - Prob. 2CQCh. 3 - Prob. 3CQCh. 3 - Prob. 4CQCh. 3 - Prob. 5CQCh. 3 - Prob. 6CQCh. 3 - Prob. 7CQCh. 3 - Prob. 8CQCh. 3 - Prob. 9CQCh. 3 - Prob. 10CQCh. 3 - Prob. 11CQCh. 3 - Prob. 12CQCh. 3 - Prob. 13CQCh. 3 - Prob. 14CQCh. 3 - Prob. 15CQCh. 3 - Prob. 16CQCh. 3 - Prob. 17CQCh. 3 - Prob. 1MCQCh. 3 - Prob. 2MCQCh. 3 - Prob. 3MCQCh. 3 - 4. A runner moves along a circular track at a...Ch. 3 - Prob. 5MCQCh. 3 - Prob. 6MCQCh. 3 - Prob. 7MCQCh. 3 - Prob. 8MCQCh. 3 - Prob. 9MCQCh. 3 - Prob. 10MCQCh. 3 - Prob. 11MCQCh. 3 - Prob. 12MCQCh. 3 - Prob. 13MCQCh. 3 - Prob. 14MCQCh. 3 - Prob. 15MCQCh. 3 - Prob. 16MCQCh. 3 - Prob. 17MCQCh. 3 - Prob. 1PCh. 3 - Prob. 2PCh. 3 - Prob. 3PCh. 3 - Prob. 4PCh. 3 - Prob. 5PCh. 3 - Prob. 6PCh. 3 - Prob. 7PCh. 3 - Prob. 8PCh. 3 - Prob. 9PCh. 3 - Prob. 10PCh. 3 - Prob. 11PCh. 3 - 12. Michaela is planning a trip in Ireland from...Ch. 3 - Prob. 13PCh. 3 - Prob. 14PCh. 3 - Prob. 15PCh. 3 - Prob. 16PCh. 3 - Prob. 17PCh. 3 - Prob. 18PCh. 3 - Prob. 19PCh. 3 - Prob. 20PCh. 3 - Prob. 21PCh. 3 - Prob. 22PCh. 3 - Prob. 23PCh. 3 - Prob. 24PCh. 3 - Prob. 25PCh. 3 - Prob. 26PCh. 3 - Prob. 27PCh. 3 - Prob. 28PCh. 3 - Prob. 29PCh. 3 - Prob. 30PCh. 3 - Prob. 31PCh. 3 - Prob. 32PCh. 3 - Prob. 33PCh. 3 - Prob. 34PCh. 3 - Prob. 35PCh. 3 - Prob. 36PCh. 3 - Prob. 37PCh. 3 - Prob. 38PCh. 3 - Prob. 39PCh. 3 - Prob. 40PCh. 3 - Prob. 41PCh. 3 - Prob. 42PCh. 3 - Prob. 43PCh. 3 - Prob. 44PCh. 3 - Prob. 45PCh. 3 - Prob. 46PCh. 3 - Prob. 47PCh. 3 - Prob. 48PCh. 3 - Prob. 49PCh. 3 - Prob. 50PCh. 3 - Prob. 51PCh. 3 - Prob. 52PCh. 3 - Prob. 53PCh. 3 - Prob. 54PCh. 3 - Prob. 55PCh. 3 - Prob. 56PCh. 3 - Prob. 57PCh. 3 - Prob. 58PCh. 3 - Prob. 59PCh. 3 - Prob. 60PCh. 3 - Prob. 61PCh. 3 - Prob. 62PCh. 3 - Prob. 63PCh. 3 - Prob. 64PCh. 3 - Prob. 65PCh. 3 - Prob. 66PCh. 3 - Prob. 67PCh. 3 - Prob. 68PCh. 3 - Prob. 69PCh. 3 - Prob. 70PCh. 3 - Prob. 71PCh. 3 - Prob. 72PCh. 3 - Prob. 73PCh. 3 - Prob. 74PCh. 3 - 75. A Nile cruise ship takes 20.8 h to go upstream...Ch. 3 - Prob. 76PCh. 3 - Prob. 77PCh. 3 - Prob. 78PCh. 3 - Prob. 79PCh. 3 - Prob. 80PCh. 3 - Prob. 81PCh. 3 - Prob. 82PCh. 3 - Prob. 83PCh. 3 - Prob. 84PCh. 3 - Prob. 85PCh. 3 - Prob. 86PCh. 3 - Prob. 87PCh. 3 - Prob. 88PCh. 3 - Prob. 89PCh. 3 - Prob. 90PCh. 3 - Prob. 91PCh. 3 - Prob. 92PCh. 3 - Prob. 93PCh. 3 - Prob. 94PCh. 3 - Prob. 95PCh. 3 - Prob. 96PCh. 3 - Prob. 97PCh. 3 - Prob. 98PCh. 3 - Prob. 99PCh. 3 - Prob. 100PCh. 3 - Prob. 101PCh. 3 - Prob. 102PCh. 3 - Prob. 103PCh. 3 - Prob. 104PCh. 3 - Prob. 105PCh. 3 - Prob. 106PCh. 3 - Prob. 107PCh. 3 - Prob. 108PCh. 3 - Prob. 109PCh. 3 - Prob. 110PCh. 3 - 111. A ball is thrown horizontally off the edge of...Ch. 3 - 112. A marble is rolled so that it is projected...Ch. 3 - Prob. 113PCh. 3 - Prob. 114PCh. 3 - Prob. 115PCh. 3 - Prob. 116P
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Text book image
University Physics (14th Edition)
Physics
ISBN:9780133969290
Author:Hugh D. Young, Roger A. Freedman
Publisher:PEARSON
Text book image
Introduction To Quantum Mechanics
Physics
ISBN:9781107189638
Author:Griffiths, David J., Schroeter, Darrell F.
Publisher:Cambridge University Press
Text book image
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:9780321820464
Author:Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:Addison-Wesley
Text book image
College Physics: A Strategic Approach (4th Editio...
Physics
ISBN:9780134609034
Author:Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:PEARSON
Vectors and 2D Motion: Crash Course Physics #4; Author: CrashCourse;https://www.youtube.com/watch?v=w3BhzYI6zXU;License: Standard YouTube License, CC-BY