Question

Can someone please help me solve this problem I don't understand A softball is thrown up into the air. The ball's height in feet is modeled by the equation h(t) = -16t2 + 32t + 5.
h = height
t = time in seconds
Find the maximum height of the ball.

a) 12.2 feet

b) 8.3 feet

c) 13.9 feet

d) 7.6 feet

Answer 1

well you see your equation is height as the time changes so imagine you throwing a ball into the air it will go up and then down
that means at the top before the ball begins to fall down it will have a positive velocity then it will will go to 0 velocity and when its velocity is negative it will begin to fall down
so that means if you take the derivative of this function derivavtive of height / t = velocity
so you take h'(t) solve for = 0 because you want to know at what time the ball went to 0 velocity then you can plug that time back into your main equation which tells you height (given time) and see what height it was at the time the velocity went to 0