Question

An object is dropped from the rest a height of 150m and simultaneously another object is dropped from the rest at a height 100m what is the diffrence Their height after 2s if both objects drop with same acceleration?how does the difference in heights vary with time

Answer 1

Hey.

Initial velocity for both the objects is 0m/s.

acceleration = 10 m/s^2

As, s = u t + 1/2 a t^2

so, s for first object in 2s

= 0+ 1/2×10×2^2 = 20 m from top

Similarly s for 2nd object will be 20m from top

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But height will be :

for 1st obj : 150-20 = 130 m

for 2nd obj : 100 -20 = 80 m

So, difference in height will be

130 -80 = 50m

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So, for fist object :

H1 = 150 - s

or, H1 = 150 - 1/2 a t^2

And for 2nd object:

H2 = 100 - s

or, H2 = 100 - 1/2 a t^2

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Verification :


For 1st obj; in 2s

H = 150 - 1/2×10×2^2 = 150-20 = 130 m

For 2nd obj: in 2s

H = 100 - 1/2×10×2^2 = 100-20 = 80 m

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So, variation of difference in height

∆H = H1-H2 = (150-1/2 at^2) -(100-1/2 at^2)

so, ∆ H = 50 m which will also remain constant with time during the flight .

Thanks .