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Question

A friend is running at a constant speed in the direction (North 75 degrees West). When he is 30 meters directly north of you, you shoot a rubber band at him in the direction (North 10 degrees East). If the rubber band travels at a constant speed and successfully strikes your friend, how fast was he running?

Answer 1

bearing 75 degrees NW

you shoot bearing 10 degrees NW (not E)

he's 30 meters due north

construct a triangle

ASA 10-30-(90-75)

angles are 10-15-(180-10-15)

sides are a-b-30

a=sin10(30)/sin155=distance the guy ran=12.33 meters= 3.28x12.33 feet

b=distance the rubberband traveled= sin15(30)/sin155=about 18.37 meters= 3.28x18.37 feet

people run from 5 to 10 mph, rubberbands go faster, about 1.5 times as fast in this problem

18.37/12.33 times as fast

if the rubberband went 10.5 mph the guy ran about 7 mph

12.33(10)/18.37=7.05 mph

average rubber band travels 10 to 20 mph

if you took the mean of 15 mph

then the guy ran 12.33(15)/18.37 = about 10.5 mph= 10.5x.45 m/sec=about 4.7 m/sec

rubber bands differ in length and width and the rubber material

fastest marathon runners do 26+ miles in 2 hours which is about 13 mph

fastest 100 meter record is about 10 meters per second = 22 mph