Gravity on a lonely planet

Classical Mechanics Level 2

Astronauts on an atmosphere-less planet wanted to find the acceleration due to gravity. And to find it, they launched a ball from the Surface of the planet, with a velocity of \(15\text{ m/s}\). And hence the astronauts predicted that the ball would reach as height of:

\[s=15t-\dfrac 12 g_pt^2\]

\(t\) seconds after the launch. If the ball reached the maximum height after \(20\) seconds. What was the value of \(g_p\)?

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