Question

A baseball will reach heighth feet artert seconds, as

h(t) = 2 + 90t - 16t^2
At what time(s) will the baseball be 76 feet high? (Explain how you got the answer/show work please).

Answer 1

1 and 37/8 feet

Explanation:

We set h(t) to 76 because we want to know when the ball will be at 76 feet high.

So, we have 76=-16t^2+90t+2. When we subtract 76 from both sides, we get -16t^2+90t-74=0, and when you mutiply the equation by -1 (so that x^2 has a positive coefficient, which makes things easier), we get 16t^2-90t+74=0.

We notice that each separate monomial has a common factor, 2, so we can take that out and make it 2(8t^2-45t+37) = 0. Factoring the quantity in the parentheses gives us 2(t-1)(8t-37) = 0.

Using Zero Product Property, we can set the two factors in parentheses to 0 (the 2 isn't really relevant so we don't need to worry about it). This gives us t-1=0 and 8t-37=0. Solving these two equations gives us t = 1 foot or t = 37/8 feet.