During the halftime of a soccer game, a sling shot 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 the T-shirt to reach its maximum height? What is the maximum height?
To find the maximum height of the T-shirt, we need to find the vertex of the quadratic equation h(t)=-16t^2+64t+6.
The vertex of a quadratic equation in the form h(t) = at^2 + bt + c can be found using the formula t = -b/2a.
In this case, a = -16 and b = 64. Plugging in these values, we have:
t = -64 / (2*(-16))
t = -64 / (-32)
t = 2
The T-shirt will reach its maximum height after 2 seconds.
To find the maximum height, we need to plug this value of t back into the equation for h(t):
h(2) = -16(2)^2 + 64(2) + 6
h(2) = -16(4) + 128 + 6
h(2) = -64 + 128 + 6
h(2) = 70
The maximum height of the T-shirt is 70 feet.