Question

An object is dropped from rest into a pit, and accelerates due to gravity at roughly 10 m/s2. It hits the ground in 5 seconds. A rock is then dropped from rest into a second pit, and hits the ground in 10 seconds. How much deeper is the second pit, compared to the first pit?

Answer 1

Second pit is 375 m deeper compared to first pit.

Step-by-step explanation:

We have equation of motion s = ut + 0.5at²

First object hits the ground after 5 seconds,

Initial velocity, u = 0 m/s

Acceleration, a = 10 m/s²

Time, t = 5 s

Substituting,

s = ut + 0.5 at²

s = 0 x 5 + 0.5 x 10 x 5²

s = 125 m

Depth of pit 1 = 125 m

Second object hits the ground after 10 seconds,

Initial velocity, u = 0 m/s

Acceleration, a = 10 m/s²

Time, t = 10 s

Substituting,

s = ut + 0.5 at²

s = 0 x 10 + 0.5 x 10 x 10²

s = 500 m

Depth of pit 2 = 500 m

Difference in depths = 500 - 125 = 375 m

Second pit is 375 m deeper compared to first pit.