Question

The height h, in feet of a model rocket t seconds after launch is given
by the equation h= 245t - 16t?. As the rocket descends, it deploys
a recovery parachute when it reaches 325 feet above the ground.
Express your final answer to the nearest tenth place.
What is the maximum height of the rocket?

Answer 1

Answer:

h_max = 324.09 ft

Step-by-step explanation:

The correct equation is;

h = 245t - 16t²

We are told that as the rocket descends, it deploys

a recovery parachute when it reaches 325 feet above the ground.

Thus;

245t - 16t² = 325

Thus;

16t² - 245t + 325 = 0

Using quadratic formula, we have the roots as;

t = 1.47s or 13.85s

We will pick the higher value.

Thus;

Maximum height will occur at t = 13.85 s

Thus, plugging in 13.85 for t into h = 245t - 16t², we have;

h_max = 245(13.85) - 16(13.85)²

h_max = 324.09 ft