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Chapter 2: Problem 3

A runner, jogging along a straight line path, starts at a position $60 \mathrm{m}$ east of a milestone marker and heads west. After a short time interval he is \(20 \mathrm{m}\) west of the mile marker. Choose east to be the positive \(x\) -direction. (a) What is the runner's displacement from his starting point? (b) What is his displacement from the milestone? (c) The runner then turns around and heads east. If at a later time the runner is \(140 \mathrm{m}\) east of the milestone, what is his displacement from the starting point at this time? (d) What is the total distance traveled from the starting point if the runner stops at the final position listed in part (c)?

Short Answer

Expert verified
The runner's displacement from his starting point is -80 m (westward). (b) What is the runner's displacement from the milestone? The runner's displacement from the milestone is -20 m (westward). (c) What is the runner's displacement from the starting point to 140m east of the milestone? The runner's displacement from the starting point to 140m east of the milestone is 80 m (eastward). (d) What is the total distance traveled by the runner from the starting point to the final position (140m east of the milestone)? The total distance traveled by the runner from the starting point to the final position is 240 m.

Step by step solution

01

(a) Find the displacement from the starting point (60m east of milestone marker) to his new position (20m west of milestone marker).

First, let's determine the runner's final position in terms of the east direction. Since the runner is 20m west of the milestone marker, and east is the positive x-direction, we have -20m as his final position. The initial position was 60m east. Displacement is final position minus initial position. Thus, the displacement from the starting point is: \((-20) - 60 = -80 \mathrm{m}\) The runner's displacement from his starting point is \(-80 \mathrm{m}\). (Note that the negative sign indicates the displacement is westward.)
02

(b) Find the displacement from the milestone

The runner is 20m west (negative direction) of the milestone. The displacement from the milestone is simply \(-20\, \mathrm{m}\) (westward).
03

(c) Calculate the displacement from the starting point to 140m east of the milestone

The current position of the runner is 140m east. We need to calculate the displacement from the starting point (60m east of the milestone marker) to this position. The displacement is simply: \(140 - 60 = 80 \mathrm{m}\) The displacement from the starting point to 140m east of the milestone is \(80 \mathrm{m}\) (eastward).
04

(d) Calculate the total distance traveled from the starting point and stopping at the final position listed in part (c)

To find the total distance traveled, we first determine the distance from the starting point (60m east) to the first location which is 20m west. The absolute value of the distance is \(80 \mathrm{m}\). Then we calculate the distance from the first location (20m west) to the final location (140m east). The difference in position is: \(140 - (-20) = 160 \mathrm{m}\) So the total distance traveled is the sum of these distances: \(80 + 160 = 240\, \mathrm{m}\) The runner has traveled a total distance of 240m from the starting point to the final position.

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