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

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.