Question

A baseball is thrown with a vertical velocity of 50 ft/s from an initial height of 6 ft. The height h in feet of the baseball can be modeled by h(t) = -16t2 + 50t + 6, where t is the time in seconds since the ball was thrown. It takes the ball approximately _____ seconds to reach its maximum height. (Round to the nearest tenth of a second and enter only the number.)

Answer 1

To find the time to reach the maximum height you can subtract the constant 6 and write the function as:

h'(t) = -16t^2 + 50t

Then factor it: h'(t) = -2t(8t-25)
Then find the two roots:
t =0 and
8t - 25 = 0 ⇒ t = 25/8 = 3.125

The vertex is in the half between 0 and 3.125, i.e. [0+3.125]/2 = 1.5625

Then the time searched is approximately 1.56 seconds.