ball speed using quadratic formula

Question

A ball is thrown vertically in the air with a velocity of 100ft/s. Use the projectile formula h=−16t2+v0t to determine at what time(s), in seconds, the ball is at a height of 150ft

Answer 1

There are two solutions: 2.5 seconds and 3.75 seconds.

h is the height of the ball, and v0 is the initial velocity that the ball is thrown at. In this case, v0 = 100 ft/s and h = 150 ft. So, the equation becomes:

150 = -16t² + 100t

If you subtract 150 from both sides, you get:

0 = -16t² + 100t - 150

Now, you can just use the quadratic formula:

x = [-b +/- √(b² - 4ac)] / (2a)

In this case, a = -16, b = 100, and c = -150. Plugging these numbers in, you get:

t = [-100 +/- √(100² - 4*(-16)*(-150)] / [2 *(-16)]

Which simplifies to:

t = (-100 +/- 20) / (-32)

So, this gives you two solutions:

t = (-100 + 20) / (-32) = (-80)/(-32) = 5/2 = 2.5 seconds

OR

t = (-100 - 20) / (-32) = (-120)/(-32) = 15/4 = 3.75 seconds

So, the ball at a height of 150 feet 2.5 seconds after it is thrown, and then again 3.75 seconds after it is thrown.