Question

A rocket is launched from a height of 3 m with an initial velocity of 15 m/s What is the maximum height of the rocket? When will this occur?
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Answer 1

If no extra acceleration is added to the rocket, then its velocity at time t is

v = 15 m/s - g t

where g = 9.80 m/s² is the magnitude of the acceleration due to gravity.

Also, recall that

v² - u² = 2 a ∆x

where u is initial speed, v is final speed, a is acceleration, and ∆x is net displacement.

At the rocket's maximum height ∆x, the velocity is 0. So, the maximum height is

0² - (15 m/s)² = 2 (-g) ∆x

∆x = (15 m/s)² / (2 * (9.80 m/s²)) ≈ 11.48 m

But this assumes the rocket is launched from the ground. We're given that the rocket is launced from 3 m above the ground, so we need to add this to the height above. So the maximum height is closer to 14.48 m.

As mentioned before, this happens when vertical velocity is 0:

0 = 15 m/s - g t

t = (15 m/s) / (9.80 m/s²) ≈ 1.53 s