Billy-joe stands on the talahatchee bridge kicking stone into the water below.
a) if billy-joe kicks a stone with a horizontal velocity of 3.5 m/s, and it lands in the water a horizontal distance of 5.4 m/s from where billy-joe is standing, what is the height of the bridge?

11.6 m

Explanation:

First of all, we need to calculate the time of flight of the stone. This can be done by analyzing the horizontal motion only, which is a uniform motion with constant velocity . The time of flight is:

where d = 5.4 m is the horizontal distance covered by the stone. Substituting,

Now we can analyze the vertical motion, which is a uniform accelerated motion with constant acceleration g = 9.8 m/s^2 downward. The vertical distance covered (which is the height of the bridge) is

where

u = 0 is the initial vertical velocity

t = 1.54 s is the time of flight

Substituting, we find