To find the time it will take for the T-shirt to reach its maximum height, we need to find the vertex of the parabolic equation h(t) = -16t^2 + 48t + 3.
The formula for the x-coordinate of the vertex of a parabola in the form y = ax^2 + bx + c is given by x = -b/2a.
In this case, a = -16 and b = 48. So, x = -48 / 2(-16) = -48 / -32 = 1.5 seconds.
Now, to find the maximum height, we substitute t = 1.5 seconds 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, it will take 1.5 seconds for the T-shirt to reach its maximum height of 39 feet.
during the halftime of a basketball game, a slingshot 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 h(t)=-16t^2+48t+3, 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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