A ball dropped from a balloon falls y=16x^2 feet in x seconds.
If the balloon is 576 feet above the ground when the ball is dropped, when does the ball hit the ground?
What is the impact velocity of the ball at the instant it hits the ground?



The answer is 6 seconds and 192 ft/s. But I don't understand how the book got that answer...

The examples the teacher showed us were totally different than this problem from the book. Why does that always happen...
Anyways, thanks in advance for the help.

put 576 in for y, what do you get for x?

Have you done differentiation? If you find the derivative of y=16x^2, and put in your value for x, you will get the speed.
This is because x^2 is the second integral of a position, and so shows an acceleration, by differentiating we get a value in terms of x and that is a speed.

Hi