Concept explainers
whether the balls ever pass each other.
Answer to Problem 46E
The balls pass each other at the time of
Explanation of Solution
Given data:
Consider the edge of cliff is at 432 ft above the ground.
Speed of first ball is
Formula Used:
Write the expression for acceleration function
Here,
Write the expression for velocity function
Here,
Antiderivative of
Calculation:
Initial velocity of first ball is
The two balls are thrown from same edge and edge of cliff is at 432 ft. Hence,
The motion of stone is close to ground, so the motion is considered as gravitational constant
Write the expression for acceleration function of first ball
Substitute
Antiderivate the expression with respect to t,
Here,
C is arbitrary constant.
Substitute 0 for t in equations (3),
Substitute 48 for
Substitute 48 for C in equation (3),
Substitute
Antiderivate the expression with respect to t,
Here,
D is arbitrary constant.
Substitute 0 for t in equation (5),
Substitute 432 for
Substitute 432 for D in equation (5),
Write the expression for acceleration function of second ball
Substitute
Antiderivate the expression with respect to t,
Substitute 1 for t in equations (6),
Substitute 24 for
Substitute 56 for C in equation (6),
Substitute
Antiderivate the expression with respect to t,
Substitute 1 for t in equation (8),
Substitute 432 for
Substitute 392 for D in equation (8),
The balls pass each other when their positions are equal.
Substitute
Thus, the balls pass each other at the time of
Chapter 4 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning