SOLUTION: The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds. How long will it

Algebra ->  Rectangles -> SOLUTION: The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds. How long will it      Log On


   

Question 654892: The height of an object thrown upward with an initial velocity of 96 feet per second is given by the formula h = −16t2 + 96t, where t is the time in seconds. How long will it take the object to reach a height of 144 feet?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
3 sec
Let t = 3
You get -16*9+96*3 = -144+288 = 144
I did this by setting the derivative of the h with respect to t equal to zero and solving for t as follows
-16*2*t + 96 = 0 or
t = 96/32 or 3
That is the highest point in the trajectory. It turns out to be 144 feet, the solution to the problem. If the highest point was less than 144', the problem would not have an answer (couldn't reach 144'). By the way it hits the ground in 6 sec.