Question

If an avalanche takes 2 seconds to fall
20 metres, how far will it fall in-,
second? If the time taken by an
avalanche to fall is proportional to the
square root of the distance it falls.​

Answer 1

Time taken ∝ √(Distance Covered)

Time taken = K √(Distance Covered)

K = Constant

Time Taken = 2 sec

Distance covered = 20 m

=> 2 = K √20

=> K = 2/√20

Time = 1/2 sec

Distance covered = D

=> 1/2 = K √D

=> 1/2 = (2/√20) √D

=> √D = √20/4

Squaring both sides

=> D = 20/16

=> D = 1.25 m

Distance covered = 1.25 m in 1/2 secs

Avalanche will fall 1.25 m in 1/2 sec if time taken is in proportion to square root of distance covered and it falls 20 m in 2 sec