Quadratic Functions

Question

NASA launches a rocket at t = 0 seconds. Its height, in meters above sea-level, as a function of time is given by h(t) = −4.9t^2 + 262t + 395.

Assuming that the rocket will splash down into the ocean, at what time does splashdown occur? (Round to the nearest tenth.)

The rocket splashes down after ___ seconds.

How high above sea-level does the rocket get at its peak? (Round to the nearest tenth.)

The rocket peaks at ___ meters above sea-level.

Answer 1

When rocket splash h(t) = -4.9t² + 262t + 395 = 0; t = 54.9 s (We use TI-84);

The rocket splash down after 54.9 s

Velocity of rocket v(t) = 262 - 9.8t = 0 at ighest point, t = 262/9.8 = 26.7 s

So, maximum height is h_max = h(26.7) = - 4.9·26.7 + 262·26.7 + 395 = 3897.2 m

The rocket peaks 3897 m above sea-level