Question

An object is dropped from rest at a height of $150m$ and simultaneously another object is dropped from rest at a height of $100m$. What is the difference in their heights after $2s$ if both the objects drop under the same acceleration? How does the difference in heights vary with time?

Answer 1

Initial difference in height = $(150–100)m=50m$
Distance travelled by first body in $2s=h_1=0+\frac{1}{2}g(2{)}^2=2g$
Distance travelled by another body in $2s=h_2=0+\frac{1}{2}g(2{)}^2=2g$
After $2s$, height at which the first body will be = $h_1=150-2g$
After $2s$, height at which the second body will be = $h_2=100-2g$
Thus, after $2s$, difference in height =$150-2g-(100-2g)$
$=50m$ = initial difference in height.
Thus, difference in height does not vary with time.