Free Fall

Instantaneous speed of a falling object can be calculated by the formula: v=gt V is velocity g is gravitational acceleration t is time (this can be the total fall or for any time during the fall)

How fast something falls is entirely different from how far it falls. d=1/2gt2 d is distance g is gravitational acceleration t is time

Example 1: How far will an object have traveled 4 seconds after it is dropped off the edge of the Grand Canyon? What would be its speed at that time?

Example 2: How long would it take a body pushed from an airplane (without a parachute) to hit the ground if the plane was 30km above ground level?

Average speed of a falling object: Usually a falling object will change speed throughout its fall due to gravity. If asked to calculate an objects average falling velocity/speed, use the following formula: Vavg= Si + Sf 2 Si is speed initial Sf is speed final

Example 3: What is the average speed of an object that is dropped from rest and reaches a maximum speed of 45m/s?

Examples 4-6: An apple drops from a tree and hits the ground in 1 second. What is its speed when it hits the ground? What is its average speed during its fall? How high above the ground was the apple when it fell?

Falling Objects

Most matter will tend toward the ground if it’s mass is less than that of air. Some exceptions: smoke, helium, hydrogen… Matter is “attracted” to earth due to gravity

All bodies of matter have attractions to other massive bodies All bodies of matter have attractions to other massive bodies. You are attracted to the person sitting next to you due to electrical and universal gravitation. BUT, the earth’s gravitational force is larger, so you do not “move” toward that other person.

All planets and solar bodies have gravitational forces as well. We will refer to this gravitational force as gravitational acceleration. ON EARTH, GRAVITATIONAL ACELERATION IS 9.81 m/s2

In 1971while on the moon, an astronaut dropped a hammer and a feather at the same time. Which hit first? Why?

We will use all of our acceleration formulas, but it will be understood that for falling objects that a=9.81m/s2 while on earth.

Example7: If a penny is dropped from the edge of a cliff that is 300m high, what is the velocity of the penny as it hits the ground?

Example 8: Using the final velocity from example 1, how long does it take for the penny to hit the ground?

Once an object has no “holder,” gravity is the only factor effecting it. The up trip is a mirror image of the down trip due to the effect of gravity.

At the top of the path the velocity is zero. Logically, if the ball is thrown with an upward velocity of Xm/s, when the ball returns to that point on its downward trip, it velocity is Xm/s. The only acceleration is due to gravity.

Examples 9-11: If Henry throws a baseball straight up with an initial velocity of 15 m/s, what is the ball’s velocity at the top of its path? How long does he have to wait for the ball to return? What is the maximum height the ball will reach over his head?