Arturo O. answered • 11/03/17

Experienced Physics Teacher for Physics Tutoring

h(t) = (-1/2)gt

^{2}+ v_{0}t + h_{0}g = 9.8 m/s

^{2}h

_{0}= 28.9 mv

_{0}= ?h(t) = -4.9t

^{2}+ v_{0}t + 28.9 [h in meters, t in seconds]Since it hits the ground at 2.71 s,

h(2.71) = 0

0 = -4.9(2.71)

^{2}+ v_{0}(2.71) + 28.9Solve for v

_{0}and getv

_{0}≅ 2.61 m/s**h(t) = -4.9t**

^{2}+ 2.61t + 28.9I suspect there may be a typo in one or more numbers in the problem statement. The equation above is correct based on launch height and time to hit ground. However, the time to maximum height should be the time at the vertex of the height vs. time parabola, which is at

t = -2.61/[2(-4.9)] s ≅ 0.266 s ≠ 0.56 s

Would you double-check the numbers in the original problem statement?