2.91) A park ranger with a tranquilizer dart gun intends to shoot a monkey hanging from a branch. The ranger points the barrel directly at the monkey, not realizing that the dart will follow a parabolic path that will pass below the present position of the creature. The monkey, seeing the gun discharge, immediately lets go of the branch and drops out of the tree, expecting to avoid the dart. (a) Show that the monkey will be hit regardless of the initial speed of the dart as long as this speed is great enough for the dart to travel the horizontal distance to the tree. Assume the reaction time of the monkey is negligible. (b) Let ~vd0 be the initial velocity of the dart relative to the monkey. Find the velocity of the dart relative to the monkey at an arbitrary time t during the dart’s flight.