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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 4.8, Problem 46E

To determine

whether the balls ever pass each other.

Expert Solution

The balls pass each other at the time of

**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