A lacrosse player throws the ball from an initial height of 7 feet with an initial velocity of 90 feet per second. t means time in seconds and h is height in feet.
how long for ball to hit ground?
Maximum height of ball?
when does the ball reach max height?
I think you have left out a t from your equation. It should be:
h(t) = -16t2 + 90t + 7
Ball hits ground when h(t) = 0
0 = -16t2 + 90t + 7
This is a quadratic in t, so t = (-90 - sqrt(902-4*(-16)*7))/(2*(-16)) or t = 5.7 s (the other root is negative so isn’t relevant here).
Maximum height of ball when dh(t)/dt = 0
dh(t)/dt = -32t + 90, so 0 = -32t + 90 or t = 2.8125 s. This gives the time the ball reaches its maximum height. Put this value into the expression for h(t) to find the value of the maximum height.