During halftime of a basketball game, a sling shot launches T-shirts at the crowd. A T-shirt is launched from a height of 4 feet with an initial upward velocity of 68 feet per second. Use the equation ht(t)-16t^2 +68t+4 , 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?
The T-shirt takes
The T-shirt's maximum height is
To find the time it takes for the T-shirt to reach its maximum height, we can use the formula for the time at the vertex of a quadratic equation, which is given by t = -b/2a. In this case, a = -16 and b = 68, so the time it takes for the T-shirt to reach its maximum height is t = -68/(2*(-16)) = 2.125 seconds.
To find the maximum height, we can substitute this value of t into the equation h(t) = -16t^2 + 68t + 4. So the maximum height is h(2.125) = -16*(2.125)^2 + 68*(2.125) + 4 = 75.125 feet.
Therefore, the T-shirt takes 2.125 seconds to reach its maximum height, and the maximum height is 75.125 feet.