A pumpkin is launched directly upwards at 72 feet per second from a platform 12 feet high. The pumpkin's height, h, at time t se conds can be represented by the equation h(t)= -16t^2+72t+12. Find the maximum height of the pumpkin and the time it takes to reach it.
1 answer:
Answer:
93 feet
Step-by-step explanation:
Let us first find the time it takes to reach the maximum height. We can do this by differentiating the height function to get velocity:
dh(t)/dt = v(t) = -32t + 72
The maximum height will occur when the velocity becomes 0. Therefore, the time it takes to reach maximum height is:
0 = -32t + 72
32t = 72
t = 72/32 = 2.25 seconds
Therefore, the maximum height of the pumpkin is:
h(2.25) = -16(2.25)^2 + 72(2.25) + 12
h(2.25) = -81 + 162 + 12
h = 93 feet
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