Question

A stone is thrown up with the speed of 30 m/s from the top of a tower of height 80 m.

The total time taken by the stone to reach the

ground is: (g = 10 m/s2)
A) 8s
B) 2s
C) 6s
D) 4s

Give a proper explanation or your answer will be reported ​

Answer 1

Given:-

→ A stone is thrown up from the top

of a tower.

→ Initial velocity of the stone (u) = 30m/s

→ Height of the tower (h') = 80m

To find:-

→ Total time taken by the stone to reach

the ground.

Solution:-

Firstly, let's calculate the maximum height reached by the stone from the top of the tower :-

=> h = u²/2g

=> h = 30×30/2×10

=> h = 900/20

=> h = 45m

Now, maximum height of stone from the ground :-

=> hₘₐₓ = h + h'

=> hₘₐₓ = 45 + 80

=> hₘₐₓ = 125m

Time taken by the stone to reach maximum height of 45 from the top of the tower (t') :-

=> v = u + gt'

=> 0 = 30 + (-10)t'

=> -30 = -10t'

=> t' = -30/-10

=> t' = 3s

Also, time taken by the stone to fall through the maximum height of 125m (t) :-

=> hₘₐₓ = ut + 1/2gt²

=> 125 = 0(t) + 1/2×10×t²

=> 125 = 5t²

=> t² = 125/5

=> t² = 25

=> t = 5s

Finally, total time taken by the stone to reach the ground :-

=> tₜₒₜₐₗ = t' + t

=> tₜₒₜₐₗ = (3 + 5)s

=> tₜₒₜₐₗ = 8s

Thus, total time taken by the stone to reach the ground is 8s [Option.A]