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Question
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 2s if both the objects drop with the same accelerations? How does the difference in heights vary with time?
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Solution
Initially, the difference in heights of two objects
= 150 m – 100 m
= 50 m
Distance travelled by the first object in 2s
h = `"ut" + 1/2 "at"^2`
= `0 + 1/2 xx 10 xx 2 xx 2`
= 20 m
Distance travelled by the second object in 2s,
h' = `"ut" + 1/2 "at"^2`
= `0 + 1/2 xx 10 xx 2 xx 2`
= 20 m
Height of first object from ground at t = 2s
= 150 m − 20 m
= 130 m
Height of second object from ground t = 2s
= 100 m − 20 m
= 80 m
∴ Difference in height after t = 2s
= 130m − 80 m
= 50 m
The difference in heights does not vary with time as long as both the objects are in motion. However, when the second object reaches the ground and the first one is still in motion, then it decreases.
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