Question

A stone dropped from the roof of a building takes 2 seconds to reach the ground. Neglecting
the air resistance, find the height of the building. Also find the velocity of the stone when it
has fallen 4.9 m

Answer 1

Answer:

The height of the building is 19.6m

The velocity of stone when it has fallen 4.9m is 9.8 m/s²

Explanation:

Let the height of the building be 'H'

As the stone is dropped from the roof the building, the initial velocity (say 'u') will be 0.

We know that the acceleration due to gravity is 9.8 m/s².

Newton's second equation of motion states that

S = ut + $\frac{1}{2}$at²

Here, S = Height of the building = H

         u = 0

          t = 2 sec

          a =  acceleration due to gravity = 9.8 m/s².

So we calculate H

=>  H = 0*2 + $\frac{1}{2}$ *9.8*2²

         = 0 + 9.8*2

         = 19.6m

Therefore the height of the building is 19.6m

We need to find the velocity when S = 4.9 m

Using Newton's third equation of motion that states that

v² = u² + 2aS

Here, S = 4.9m

         u = 0

          a =  acceleration due to gravity = 9.8 m/s².

Substituting the values,

v² = 0² + 2*9.8*4.9

v² = 0 + 9.8*9.8

v² = 9.8*9.8

v = √9.8*9.8

v = 9.8 m/s²

Therefore the velocity of stone when it has fallen 4.9m is 9.8 m/s²

Illustration attached below.