Question

A ball is dropped from the top of a tower hundred metre high. Simultaneously another ball is thrown upwards with a speed of 50 m/s. After what time do they cross each other.

Answer 1

let us assume that they cross each other after 't' seconds at a distance of 'x' at maximum height.

in case of freely falling body(FFB),
u=0
g=10m/s²
s=x m

in case of vertically projected body(VPB)
u=50m/s
s=100-x m
g= - 10m/s
t= t sec

In case of FFB,
s=ut + 1/2at²
x= 1/2 × 10× t²
x= 5t²-------- eq.1

in case of VPB
s=ut + 1/2at²
100-x= 50 x t - 1/2 × 10 × t²
100-x= 50×t - 5t²
100-x= 50 × t -x   (from eq.1)
⇒t= 2 sec
From eq.1
x= 5 × t²
x= 20m
from the max height, 100-20 = 80m from the ground

∴ they cross each other at 80m from the ground.