Question

A bolt is dropped from a bridge under construction, falling 81 m to the valley below the bridge. (a) How much time does it take to pass through the last 30 % of its fall? What is its speed (b) when it begins that last 30 % of its fall and (c) just before it reaches the ground?

Answer 1

a) Last 30% of the fall = 0.3 of 81 = 24.3 m

First 70% of the fall = 0.7*81 = 56.7 m

Now, the bolt is dropped hence initial velocity is u = 0

Time taken for the 81m fall is

81 = 0 + (1/2)(9.8)t^2

81 = 4.9t^2

=> t = 4.065 seconds

Now, time taken for 56.7 m is

56.7 = 0 + (1/2)(9.8)t^2

t = 3.402 seconds

Hence, time taken for the last 30% fall is 4.065 - 3.402 = 0.663 seconds

b) Time taken for 56.7 m is 3.402 seconds. At the end of 56.7 m, the bolt begins the last 30% fall. Hence, from 1st equation of motion,

v = u + gt

v = 0 + 9.8*3.402

v = 33.33 m/s

c) Total time of flight is 4.065 seconds.

Hence, the speed just before reaching the ground is,

v = 0 + 9.8*4.065

v = 39.837 m/s