SOLUTION: A ball is thrown in the air with an initial velocity of 80 ft/sec. The path of the ball can be modeled by the equation h(t)=-16t^2+80t. What is the reasonable domain for the time t

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Question 719148: A ball is thrown in the air with an initial velocity of 80 ft/sec. The path of the ball can be modeled by the equation h(t)=-16t^2+80t. What is the reasonable domain for the time the ball is in the air?
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
The reasonable domain would be from the time the ball is thrown, t = 0, until the time the ball comes back to the ground. When the ball comes back to the ground, its height will be 0. So to find this time we need to solve:

Factoring we get:

From the Zero Product Property:
16t = 0 or -t+5 = 0
Solving these:
t = 0 or t = 5
We already knew about t = 0. That is when the ball is initially thrown. The t = 5 must be when it comes back to the ground. So the reasonable domain for the time would be all real numbers between 0 and 5.
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