if you want to double the length of the time interval during which the ball stays in the air above the launch position, to what maximum height do you have to throw it?

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26-10-2022
Physics

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if you want to double the length of the time interval during which the ball stays in the air above the launch position, to what maximum height do you have to throw it?

Answer :

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ayune ayune · Answer 1 · 2022-10-29T04:43:09-04:00

Based on the given parameters, to double the length of the time interval during which the ball stays in the air above the launch position, the ball should be thrown 4 times of the initial maximum height.

Let:

vo = initial velocity

hm = maximum height

tm = time to reach the maximum height

g = gravitational acceleration

Then, the following equations apply:

vo² = 2g . hm

vo = g . tm

From the above equations:

vo² is directly proportional to hm

vo is directly proportional to tm

Therefore,

tm² is directly proportional to hm

Or,

tm₂² : tm₁² = hm₂ : hm₁

From the problem, we know that:

tm₂ = 2 tm₁

Hence,

(2 tm₁)² : tm₁² = hm₂ : hm₁

4 : 1 = hm₂ : hm₁

Which means: hm₂ = 4hm₁

Or to double the time, the maximum height should be 4 times the initial maximum height.

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