There are several ways to do this question. We know that when t = 0, h = 5. By substituting t = 0 into your equation
we get c = 5. We also know that v = 15. Hence h = -16t^2 + 15t + 5. As this is
a quadratic we know that when we graph it we will get a parabola. At the top of the path
we know that the slope of the parabola is 0. Hence the derivative must be equal
to 0.
Therefore:dh/dt = -32t + 15 = 0. -32t = -15 t = -15/-32 t = 0.4665 seconds. Alternatively you could use one of the equations of
motion. I would use the equation v = u + at, where v is the final velocity, u
is the initial velocity, a is the acceleration due to gravity and t is the
time.
We know that at the top of the football's path the
velocity is 0m/s. We also know that acceleration is constant (-9.8m/s^2) and
that the initial velocity is 4.572m/s (which is equal to 15ft/s, but I am used
to working in m/s).Hence 0 = 4.572 – 9.8t -4.572 =
-9.8t t = 0.4665 seconds.
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