Question

Marie shoots an arrow vertically upward at a sandhill crane. If the arrow travels to a maximum height of 99.5 meters, calculate how fast it was shot.
And, for how much time was Marie's arrow in the air?

Answer 1

v = Vi - 9.8 t
0 = Vi - 9.8 t
Vi = 9.8 t

99.5 = Vi t -4.9 t^2
99.5 = 9.8 t^2 - 4.9 t^2 = 4.9 t^2
t = 4.5 seconds to top
so
Vi = 9.8 * 4.5 = 44.2 m/s

You could also do this by conservation of energy
(1/2) m Vi^2 = m g h
so
Vi = sqrt (2*9.8*99.5)
= 44.2 m/s