Solving average velocity

Question

The deck of a bridge is suspended 225 feet above a river. If a pebble falls off the side of the bridge, the height, in feet, of the pebble above the water surface after t seconds is given by y = 225 − 16t².

Answer 1

If your question is, "what is the average velocity of the pebble from the time it falls to the time it hits the ground?" then you would solve it as follows:

Average velocity = (v_final - v_initial)/2

V_initial = 0 since the pebble is "falling", we can assume it didn't get a push or anything.

To find the final velocity, let's first find the time it takes to hit the ground. In other words, what is "t" when y = 0?

0 = 225 - 16t²

16t² = 225

t² = 225/16

t = 15/4 = 3.75 seconds

Velocity would be the derivative of position so dy/dt = -32t = -32(3.75) = -120 ft/s

So the average velocity = (-120 - 0)/2 = -60 ft/s