To find the maximum height, we need to find the vertex of the parabolic function h(t) = -16t^2 + 72t + 5. The vertex is located at t = -b/2a, where a = -16 and b = 72.
t = -b/2a = -72/(2(-16)) = 2.25
So the maximum height is reached at t = 2.25 seconds. To find the height at this time, we plug in t = 2.25 into the equation:
h(2.25) = -16(2.25)^2 + 72(2.25) + 5 = 89.125
Therefore, the T-shirt reaches its maximum height of 89.125 feet after 2.25 seconds.
During halftime of a basketball game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 5 feet with an initial upward velocity of 72 feet per second. Use the equation h(t) =-16t^2+72t+5, where t is time in seconds and h(t) is height. How long will it take the T-shirt to reach its maximum height? What is the maximum height?
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