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Question

for a body falling from rest (Disregarding air resistance), the distance the body falls varies directly as the square of the time. If an object is dropped from the top of a tower 128 feet high and hits the ground in 4 seconds, how far did it fall in the first 2 seconds? 

Answer 1

 

Distance varies directly with square of time.

D = Kt²

 

in 4 seconds it falls 128'

Use this to solve for k

 

128 = k(4)²

128 = 16k

k = 8

 

Using this value of k, the equation becomes

D = 8t²

 

In 2 seconds

D = 8(2)²

 

D = 8 (4) = 32

The object falls 32 feet in 2 seconds.