Question

a stone is dropped from the top of a 30m high cliff. at the same instant another stone is projectd vertically upwards from the group with a speed 30 m/s. the stone will cross each other after what time?

Answer 1

ince,S=ut+1/2 at^2.

In case of free fall S=ut+1/2gt^2 eqn…1

Two cases arises here,

Case:1- stone is dropped from the tower,

given

S1=200 meters , u=0

So that, S1=ut+1/2 at^2 since it's case of free fall

So, S=ut+1/2gt^2 => S=1/2gt^2 eqn..2

Case:2 stone projected upward

S2=50t-1/2 gt^2. eqn ..3

Total distance S=S1+S2

Or, 200=S1+S2

Or, 200=1/2 gt^2+50t-1/2gt^2

=> 200=50t=> t=4sec.

Put t=4 in eqn 2.

We have, S1=0+1/2gt^2 => 1/2×9.81×4^2= 78.48m.

And S2=50×4–1/2×9.81×4×4

=200–78.48=121.52m

Both stones meet from ground in air at the distance of 121.52m in 4s.