I shoot an arrow at 59 m/s horizontally off a building trying to hit a pigeon 21 m away. How far below me is the pigeon before getting hit by my arrow?

Answer 1

I assume the 21 m is a horizontal distance, otherwise this gets very complicated. The end result shows a very small vertical displacement, so assuming Δx = 21 is very accurate anyway.

Horizontal velocity remains constant in kinematic problems, so the average velocity equals initial velocity and Δx = v_x t, 21 = 59 t, t = 0.35₆ (I keep at least 1 more digit than is significant to avoid round-off error).

Now use this equation: Δy = v₀ t + 1/2 a t², where v₀ = 0 because initially there was no vertical motion; Δy = 0 - 9.8/2 t² = -0.62 m.