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

well, max height occurs when the velocity is zero (has to stop going up before it can start down). The speed is the derivative of position with respect to time\[\frac {dh(t)} {dt}=v=-32t+50\]This must equal zero, so\[50=32t\]or\[t=50/32\sec\]then just round