If I shot an arrow an arrow straight up into the air, it would leave my bow trav

Question

If I shot an arrow an arrow straight up into the air, it would leave my bow traveling at a rate of 100 feet per second. Assume that the arrow is so "slick", that there is no friction (or air resistance). Without gravity it would continue to travel at this speed. After 12 seconds it would have traveled 12*100 feet. But, gravity will pull it back to the earth. The gravitational pull is measured as 16t2. So the height at any time t can be measured by the function  h(t) = 100t - 16t2.   

At what time t will the arrow reach it's maximum height

Explanation / Answer

To find the time for the maximum using calculus, take the derivative and set equal to zero

h'(t) = 100 - 32t

0 = 100 - 32t

32t = 100

t = 100/32 = 3.125

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