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h(t)=-16^2+90t+7

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?

Guest Apr 6, 2018

#1**+2 **

I think you have left out a t from your equation. It should be:

h(t) = -16t^{2} + 90t + 7

Ball hits ground when h(t) = 0

0 = -16t^{2} + 90t + 7

This is a quadratic in t, so t = (-90 - sqrt(90^{2}-4*(-16)*7))/(2*(-16)) or t = 5.7 s (the other root is negative so isnâ€™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.

Alan Apr 6, 2018