Question

A rocket carrying fireworks is launched from a hill 80 feet above a lake. The rocket will fall into the lake after exploding at its maximum height. The rocket's height above the surface of the lake is given by h=-16t^2+64t+80.

-what is the height of the rocket after 1.5 seconds?
-what is the maximum height reached by the rocket?
-how long will it take for the rocket to hit 128 ft?
-after how many seconds after its launched will the rocket hit the lake?

Answer 1

For first question, you can let t=1.5 and calculate h=140 ft. For second question, we can change the equation to the form of h=-16[(t-2)^2-9]. So you can see from the equation that the maximum height is created when t=2, equals to 144 ft. For question 3, let h=128. From equation, we can get t=3 or t=1. For last question, the rocket hit the lake means h=0, so t=5 or t=-1(not applicable). So the answer is t=5. You can also draw the graphic for the equation to help.