(a). If a 100m male sprinter with a velocity of 10.29 m/s and a 100m female spri
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Question
(a). If a 100m male sprinter with a velocity of 10.29 m/s and a 100m female sprinter with a velocity of 8.31 m/s were placed at opposite ends of the 100m track and both ran towards each other, where and when would they collide?
(b). if an average male 400m sprinter with a velocity of 9.24 m/s is always running at the average speed and the average female 400m runner with a velocity of 8.31 m/s starts at her average speed, what will her acceleration need to be to make sure they tie at the end of the 400m race?
(c) A 100m sprinter with a velocity of 9.35 m/s challenges gravity to a race. Your lecturer drops a bowling ball from a height of 100m at the same time the sprinter starts running 100m at their velocity. WHo wins the race and by how much?
Explanation / Answer
(A) suppose they meet after time t.
then d = 10.29t + 8.31t = 100
t = 100 / 18.6 = 5.38 sec
so they meet after 5.38 sec.
at distance of 10.29 x 5.38 = 55.3 m from male sprinter's starting point.
(B) time taken by male sprinter,
t = 400 / 9.24 = 43.29 sec
for female :
d = v0 t + a t^2 /2
400 = (8.31 x 43.29) + (a x 43.29^2 / 2)
400 = 359.74 + 937a
a = 0.043 m/s^2
(C) time taken by ball to drop 100 m.
d = g t^2 / 2
t = sqrt(2 x 100 / 9.81) = 4.52 sec
by sprinter:
t = 100 / 9.35 = 10.7 sec
hence ball wins the race.
by 6.2 sec
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