After running for 2 minutes how far east of his starting poi
After running for 2 minutes, how far east of his starting point is George? (Round your answer to three decimal places.) ft
Solution
After 14 seconds they pass each other whic means sum of distance travelled when they
pass each = semi circle length
George speed = 9 ft/sec
Distance travelled by George =9*14 = 126 feet
Paula speed = 2pi*r/40 ft/sec where r is radius of circular track
Now , 126 +pi*r/20 = pi*r
19pi*r/20 = 126
r = 42.22 ft
George would run in 2 minute = 9*120 = 1080 ft = 4 complete rounds + 18.89 ft
arc length = rø, so ø = arc length / r = 18.89/42.22 = 0.4475 radians
consider a right angled triangle in the second quadrant with hypotenuse r and angle 0.4475
cosø = adj side / r
adj side = 38.06 ft
total distance east, since he started from the westernmost point, is r - adj side = 42.22 - 38.06 = 4.157 ft
