NASA launches a rocket at t = 0 t=0 seconds. Its height, in meters above sea-level, as

NASA launches a rocket at $t=0$ seconds. Its height, in meters above sea-level, as a function of time is given by $h\left(t\right)=-4.9t^2+52t+381$.

Assuming that the rocket will splash down into the ocean, at what time does splashdown occur?

The rocket splashes down after   seconds.

How high above sea-level does the rocket get at its peak?

The rocket peaks at   meters above sea-level.