Question

The function f (t) =-16t^2 = 576 represents the height of a freely falling ballast bag that starts from rest on a ballon 576 feet above the ground. After how many seconds t does the ballast bag hit the ground.

Answer 1

Answer:

The ballast bag hits the ground after 6 seconds.

Step-by-step explanation:

Suppose there was a small typing mistake.

The height of the ball, after t seconds, is given by the following equation:

$f(t) = -16t^{2} + 576$

After how many seconds t does the ballast bag hit the ground.

This is t for which f(t) = 0. So

$f(t) = -16t^{2} + 576$

$-16t^{2} + 576 = 0$

$16t^{2} = 576$

$t^{2} = \frac{576}{16}$

$t^{2} = 36$

$t = \pm \sqrt{36}$

Time is a positive measure, so

$t = 6$

The ballast bag hits the ground after 6 seconds.