Question

During halftime of a basketball game, a slingshot launches T-shirts at the crowd. A teacher is launched from a height of 5 feet with an initial upward velocity of 72 ft./s. Use the equation h(t)=-16t^2+72t+5, where r is time in seconds and h(t) is height. How long Will it take the T-shirt to reach its maximum height? What is the maximum height?

Answer 1

2.25 seconds, 86 feet.

Explanation:

No idea where the r, second is, so I'm assuming that t is time in seconds.

Because this is a perfect parabola, we can find the zeroes (the places where the y value is 5, because that's where the teacher is launched from) and then get the middle of those 2 points.

First let's make the a term of this equation be positive so multiply everything by minus one.

16t^2-72t-5

After that, let's factor this (I won't go into details about this, you should already know how to do this if your asking this question)

we get t(t - 4.5) = 5

So the 2 x values are 0 and 4.5, and the whole flight time of the teacher is 4.5 seconds.

The half way between that is 2.25, and then we can plug that time back in to the equation to get a y value of 86.