To find the time it takes for the T-shirt to reach its maximum height, we need to determine the vertex of the parabolic function represented by the equation h(t) = -16t^2 + 48t + 3.
The time to reach the maximum height can be found using the formula t = -b/2a, where a is the coefficient of t^2, b is the coefficient of t, and c is the constant.
In this case, a = -16 and b = 48, so the time to reach the maximum height is t = -48 / 2(-16) = 1.5 seconds.
Therefore, it will take the T-shirt 1.5 seconds to reach its maximum height.
To find the maximum height, we substitute t = 1.5 into the equation h(t) = -16t^2 + 48t + 3.
h(1.5) = -16(1.5)^2 + 48(1.5) + 3
h(1.5) = -16(2.25) + 72 + 3
h(1.5) = -36 + 72 + 3
h(1.5) = 39 feet
Therefore, the T-shirt's maximum height is 39 feet above the court.
During the halftime of a basketball game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 3 feet with an initial upward velocity of 48 feet per second. Use the equation %0D%0Aℎ%0D%0A(%0D%0A𝑡%0D%0A)%0D%0A %0D%0A=%0D%0A %0D%0A−%0D%0A16%0D%0A𝑡%0D%0A2%0D%0A+%0D%0A48%0D%0A𝑡%0D%0A+%0D%0A3%0D%0Ah(t) = −16t %0D%0A2%0D%0A +48t+3 , 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?%0D%0A%0D%0A%0D%0A%0D%0AThe T-shirt takes %0D%0A%0D%0A second(s) to reach its maximum height. %0D%0A%0D%0A(If necessary, round your answer to one decimal place.)%0D%0A%0D%0A%0D%0A%0D%0AThe T-shirt's maximum height is %0D%0A%0D%0A feet above the court. %0D%0A%0D%0A(If necessary, round your answer to the nearest whole number.)
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