To find the time it will take to reach the maximum height, we need to find the vertex of the parabolic function h(t)=-16t^2+64t+6. The time to reach the maximum height can be found using the formula for the x-coordinate of the vertex, which is given by t = -b/(2a), where a = -16 and b = 64.
t = -b/(2a)
t = -64/(2*-16)
t = -64/-32
t = 2 seconds
Now, substitute t = 2 seconds back into the equation h(t) to find the maximum height:
h(2) = -16(2)^2 + 64(2) + 6
h(2) = -16(4) + 128 + 6
h(2) = -64 + 128 + 6
h(2) = 70 feet
Therefore, it will take 2 seconds for the T-shirt to reach its maximum height of 70 feet.
during the halftime of a soccer game, a slingshot launches T-shirts at the crowd. A T-shirt is launched from a height of 6 feet with an initial upward velocity of 64 feet per second. use the equation h(t)=-16t^2+64t+6, where t is time in seconds and h(t) is height. How long will it take to reach its maximum height? what is the maximum height?
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