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

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.

Alan  Apr 6, 2018

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