Question

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A ball is thrown into the air with an initial upward velocity of 48 ft/s. It height h in feet after t seconds is given by the function h (t)=-16t^2+48t+4.

In how many seconds will the ball reach its maximum height?

Answer 1

Explanation:

h(t)=-16t^2+48t+4

dh/dt=-32t+48

d2h/dt2=-32

Since acceleration is always negative when the velocity, dh/dt=0, it will occur at the maximum height.

dh/dt=0 when

-32t+48=0

-32t=-48

t=1.5 seconds

Without calculus, the vertex of a parabola will be at -b/(2a) of the quadratic equation. In this case

-48/(2(-16))

-48/-32

1.5 seconds