An object is dropped from rest at a height of 150 m and simultaneously another object is dropped from rest at a height of 100 m. What is the difference in their heights after 2 s if both the objects drop with same accelerations? How does the difference in heights vary with time?
Step 1: Given that:
The objects are dropped from rest that is
The initial velocity of both objects = u1=u2=0
Height from which the fist object is dropped= H1=150m
Height from which the second object is dropped at the same time= H2=100m
Acceleration ion first body= Acceleration in the other body
Given time(t) = 2sec
Step 2: Calculation of the distance covered by both the bodies in 2sec:
The distance covered by a body in downward direction under acceleration due to gravity that is g is given by;
h=ut+12gt2
For u=0
h=0+12gt2
h=12gt2
Now,
The distance travelled by the first body in 2s will be;
h1=12g×(2s)2
h1=12g×4
h1=2g
The distance travelled by the other body in the same 2s will be given by;
h2=12g×(2s)2
h2=12g×4
h2=2g
Step 3: Calculation of the difference in their heights after 2s:
The difference in the heights of both the bodies initially is given by;
=H1−H2
=150m−100m
=50m
After 2s,
The height at which the first body will be given by;
=H1−h1
=150m−2g
=150−2g
The height at which the other body will be given by;
=H2−h1
=100m−2g
=100−2g
Now,
=(H1−h1)−(H2−h2)
=(150−2g)−(100−2g)
=150−2g−100+2g
=50m
Which is the same as the difference in their heights initially.It is clear that the difference in their heights is 50m and it does not vary with time.
Thus,
Option C) 50m is the correct option.