Application (Quadratic Functions)

Michigan State University - Diagnostic Exam

The height h in feet of a ball thrown upward at b feet per second is $h = - 16t2 + bt + c$ , where t is time in seconds and c is the initial height in feet above the ground. If a ball is thrown upward at 24 feet per second from an initial height of 40 feet, in how many seconds will it hit the ground?

a) 1 sec. b) 1.5 sec. c) 2 sec. d) 2.5 sec. e) 3 sec.

Solution:

We set $h = - 16t2 + 24t + 40 = 0$ and solve for t. Thus

2 2 - 16t + 24t + 40 = 0 ⇒ 2t - 3t - 5 ⇒ (2t - 5)(t + 1) = 0 ⇒ t = - 1, 5∕2

It follows that the ball hits the ground after 2.5 seconds.

Diagnostic:

July 15, 2008