Question

You can shoot an arrow straight up so that it reaches the top of a 30-m-tall building. The arrow starts 1.45 m above the ground. How far will the arrow travel if you shoot it horizontally while pulling the bow in the same way?

Answer 1

30 – 1.45 = 28.55 meters

As the arrow rises this distance, its decreases at the rate of 9.8 m//s each second. At its maximum height, its velocity is 0 m/s. Use the following equation to determine its initial velocity.

vf^2 = vi^2 + 2 * a * d, a = -9.8

0 = vi^2 + 2 * -9.8 * 28.55

vi = √559.58

This is approximately 23.66 m/s

To determine the horizontal distance it moves, we need to determine the time for it to fall 1.45 meters. Let’s use the following equation.

d = vi * t + ½ * a * t^2

vi is the initial vertical velocity. Since the arrow is moving horizontally, this is 0 m/s.

1.45 = ½ * 9.8 * t^2

t = √(1.45/4.9)

This is approximately 0.544 seconds

d = vt = 23.66 *0.544

This is approximately 12.87 meters.