Problema Solution
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 provided by our tutors
we need to find the maximum of the parabolic function:
h(t) = -16t^2 + 50t + 6
since the quotient in front of t^2 is -16<0 the function has maximum in the the vertex:
h max = c - b^2/4a, for t max = -b/2a
t max = -50/(2*(-16))
t max = 1.6 s
It takes the ball approximately 1.6 seconds to reach its maximum height.