Question

A stone is thrown upwards from the top of a tower 85 m high . It reaches the ground in 5s . Calculate

1) the greatest height above the ground

2) the velocity with which it reaches the ground

3) the time taken to reach the maximum height.(g=10 m/ s^{​​​​​​2})

Answer 1

The stone is thrown upward from the top of tower which is 85m high
It reaches the ground in 5 sec
let initial velocity be u
the displacement is -85m and acceleration is -10m/sec^2 as they are downward so the negative sign.
using
S = ut + 1/2 at^2
-85 = 5u - 1/2 x 10 x 5^2
-85 = 5u - 125
5u= 40
u=8m/sec

1) At the greatest height above the ground, the stone comes to momentary rest. so velocity becomes zero
using v^2 = u^2 + 2as
or 0 = 8^2 + 2x -10 x s
or 0= 64 - 20s
or s = 3.2 m
thus the maximum height from the ground is 3.2+85 = 88.2m

2) Velocity with which it reaches the ground is
v = u + at
or v = 8 - 10x5 = -42m/sec (downward)

3) to reach maximum height it will take time = u/g = 8/10 = 0.8 second.