Use Problem Solving Skills to answer the following question.
The projected path of Donovan's touchdown pass is represented by the following function:
h = -t2 + 5t, where h represents the height of the ball after t seconds.
How much time is the ball in the air before it hits the ground?
1. Identify the Problem
Problem: How much time is the ball in the air before it hits the ground?
Unit: Seconds
2. Identify What You Know
- h = height of the ball
- t = number of seconds that pass after the ball is thrown
- h= -t2 + 5t
- When the ball hits the ground, h = 0
4. Carry out the Plan
0 = -t2 + 5t, Solve for t.
- 0 = t(-t + 5)
- 0 = t
- 0 = -t + 5
- 5 = t
The ball hits the ground at 0 seconds and 5 seconds.
5. Verify That the Answer Makes Sense
Plug in t = 0 into the function:
- 0 = -t2 + 5t
- 0 = -(0)2 + 5(0)
- 0 = 0 + 0
- 0 = 0
Plug in t = 5 into the function:
- 0 = -t2 + 5t
- 0 = -(5)2 + 5(5)
- 0 = -25 + 25
- 0 = 0
Note: -(5)2 is not positive 25.
Can the ball hit the ground after 0 seconds? No. Can the ball hit the ground after 5 seconds? Yes.
Does the answer, 5 seconds, answer the question? Yes.