Question

A toy rocket is fired into the air from the top of a barn. It's height h in yards above the ground after t seconds is given by the function H(t)=-3t2+12t+24 what is the height of the barn? Include units! When did the rocket reach its maximum height? Include units what was the maximum height of the rocket? Include units

Answer 1

Answer:

The rocket reached its maximum height at 2 seconds.

The maximum height of the rocket is 36 yards.

Step-by-step explanation:

Quadratic equation:

In the format

$h(t) = ah^{2} + bh + c$

The maximum height happens at the instant of time:

$t_{v} = -\frac{b}{2a}$

The maximu height is $h(t_{v})$

In this question:

$H(t) = -3t^{2} + 12t + 24$

So $a = -3, b = 12, c = 24$

When did the rocket reach its maximum height?

$t_{v} = -\frac{12}{2*(-3)} = 2$

The rocket reached its maximum height at 2 seconds.

What was the maximum height of the rocket?

H(2).

$H(2) = -3*2^{2} + 12*2 + 24 = 36$

The maximum height of the rocket is 36 yards.