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 $g_p?$