   Chapter 2, Problem 19P

Chapter
Section
Textbook Problem

Runner A is initially 4.0 mi west of a flagpole and is running with a constant velocity of 6.0 mi/h due east. Runner B is initially 3.0 mi east of the flagpole and is running with a constant velocity of 5.0 mi/h due west. How far are the runners from the flagpole when they meet?

To determine
The position at which the runners meet.

Explanation

Given Info:

The initial position of runner A is 4.0mi

The initial position of runner B is 3.0mi

The velocity of runner A is 6.0mi/h

The velocity of runner B is 5.0mi/h

Explanation:

The formula used to calculate the position of runner A when he meet runner B is,

x=x0A+vAt (I)

• x is the position at which the runners meet
• vA is the velocity of runner A
• x0A is the initial position of runner A
• t is the time taken by the runners to meet

The formula used to calculate the position of runner B when he meet runner A is,

x=x0B+vBt (II)

• x is the position at which the runners meet
• vB is the velocity of runner B
• x0B is the initial position of runner B
• t is the time taken by the runners to meet

From equations I and II, equate the position of the runners.

x0A+vAt=x0B+vBt

Rearrange the equation in terms of the time. The time taken to reach the position is,

t=x0Ax0B(vBvA)

Substitute t=(x0Ax0B)/(vBvA) for t in equation I to determine x

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