How far will the water bottle have traveled horizontally when it hits the ground?

Question

A hang glider is travelling horizontally at 14 m/s and is located 327 m above the surface of the earth. Suddenly and accidentally a water bottle falls from it. How far will the water bottle have traveled horizontally when it hits the ground? 

Answer 1

Hi Kristyn B.,

To find the horizontal distance we can use x = v_ot. We know the initial velocity but we need to know the time t, which is the same amount of time it takes the bottle to hit the ground.

To get t, we'll use the equation for the falling (y direction) bottle which is y = y_o + v_ot + 1/2 at², and solve for t. If we choose the positive y direction to be up then y = 0, y_o = 327 m, v_o = 0, and a = -g (in the -y down direction).

0 = 327 m - 4.9 m/s² * t²

4.9 m/s² * t² = 327 m

t = ±[ 327 m/4.9 m/s² ]^1/2

t = ± 8.16 s or +8.2 s (choose positive seconds)

We now have the time for the fall which is the same time the horizontal velocity has to travel.

x = 14 m/s * 8.2 s = 114 m (the horizontal distance)