When a baseball is hit by a batter, the height of the ball, h(t), at time t, is determined by the equation h(t) = -16t^2+32t+5.

Question

At what time is the ball at a height of 13 feet?

Answer 1

h(t) = 13 feet = -16t^2 + 32t + 5

Subtracting 13 from both sides of the above equation:

-16t^2 + 32t - 8 = 0

Solve using the quadratic formula:

t = 1 ± 0.5√2 seconds

or, as decimal approximations,

t = 0.292893 seconds

and

t = 1.70711 seconds