In a Punkin’ Chunkin’ contest, the height (in feet) of shots from one pumpkin cannon is given by the function \( h(t) = -16(t - 5)^2 + 425 \). The height is in feet above the ground and the time is in seconds after the pumpkin leaves the cannon. Use this function to answer questions about the height of the flying pumpkin.
a. At what height is the pumpkin released from the “chunker”?
b. At what time will the pumpkin hit the ground?
c. At what time does the pumpkin reach its maximum height and what is that height?
Answer (2)
a. At t=0, the pumpkin is 25 feet above the ground (Plug 0 into the equation and solve)
b. If you plug the equation in a graphing calculator and find the rightmost zero, you get t = 10.15 seconds.
c. The vertex (maximum point) of the graph is (5, 425). Therefore, the pumpkin reaches its maximum height of 425 feet after 5 seconds in the air.
The pumpkin is released at a height of 25 feet. It hits the ground at approximately 10.15 seconds after launch. The maximum height of 425 feet is reached at 5 seconds.
;
