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Question 945132: Benjamin threw a rock straight up from a cliff that was 120 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation h=-16t^2+76t+120, how long will it take for the rock to hit the water?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Benjamin threw a rock straight up from a cliff that was 120 ft above the water. If the height of the rock h, in feet, after t seconds is given by the equation h=-16t^2+76t+120, how long will it take for the rock to hit the water?
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When the rock hits the water it's height = 0, therefore:
-16t^2 + 76t + 120 = 0
simplify, divide equation by -4
4t^2 - 19t - 30 = 0
we can use the quadratic formula to solve this, a=4; b=-19; c=-30;
but this will factor to
(4t + 5)(x - 6) = 0
the positive solution is all we want here
t = 6 sec to hit the water
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Confirm this for yourself, calculate
h = -16(6^2) + 76(6) + 120
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