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?

Answer:

When two objects fall with the same acceleration simultaneously, after 2 seconds the difference in their heights will not change and it remains 50 m.

d1 = h1 – s1

d1 = 150 – 1/2at2

d1 = 150 – [1/2 × 10 × 4]

d1 = 150 – 20

d1 = 130 m

Therefore the height of the first object after 2 seconds is 130 m.

In the same way, the height of the second object is

d2 = h2 – s2

d2 = 100 – 1/2 at2

d2 = 100 – [1/2 × 10 × 4]

d2 =100 – 20

d2 = 80 m

Therefore, the height of the second object after 2 seconds is 80 m.

d1 – d2 = 130 m – 80 m

d1 – d2 = 50 m

So, the difference is the same, i.e. 50 m.

This concludes that the difference in height of the two objects does not depend on time and will always be the same.

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