Question

An object is dropped from rest at a height of 150 m and simultaneously another object is dropped from rest at a height 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?

• A. 50m
• B. 9.8m
• C. 0
• D. 19.6m

Answer 1

Answer: (C)

0

Initial difference in height $=(150-100)m=50m$

We know that, by second equation of kinematics, $s=ut+\frac{1}{2}a{t}^2$

considering $g=10m/s$

Distance travelled by first body in $2s=h1=0+\left(\frac{1}{2}\right)g(2{)}^2=2g=2\times 10=20m$

Distance travelled by another body in $2s=h2=0+\left(\frac{1}{2}\right)g(2{)}^2=2g=2\times 10=20m$

After $2s$, height at which the first body will be $=h_1=150-20=130m$

After $2s$, height at which the second body will be $=h_2=100-20=80m$

Thus, after 2 s, difference in height $=(130-80)$

$=50m=$initial difference in height

Thus, difference in height does not vary with time. So the answer is zero.