Question

4 in which of the following situations would the objects displacement be greater than 15 miles? a traveling east 20 miles, then west for 14 miles b traveling south 3 miles, then west 3 miles c traveling west 6 miles, east 2 miles, then west 12 miles d traveling east 12 miles, west 6 miles, then east 4 miles

Explanation:

Step1: Calculate displacement for option A

Displacement is the net distance from the starting point. If we consider east as positive and west as negative.
For option A: \(20 - 14=6\) miles (east).

Step2: Calculate displacement for option B

Using the Pythagorean theorem \(d=\sqrt{3^{2}+3^{2}}=\sqrt{9 + 9}=\sqrt{18}\approx4.24\) miles.

Step3: Calculate displacement for option C

If west is negative and east is positive. Displacement \(=-6+2-12=-16\) miles (magnitude \(16\) miles).

Step4: Calculate displacement for option D

Displacement \(=12-6 + 4=10\) miles (east).

Answer:

C. Traveling west 6 miles, east 2 miles, then west 12 miles