Astronauts on an atmosphere-less planet wanted to find the acceleration due to gravity. In order to find it, they launched a ball from the surface of the planet, with a velocity of \(15\text{ m/s},\) and predicted that the ball would reach a height of \[s=15t-\dfrac 12 g_pt^2\] meters \(t\) 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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