Aim: How can we solve free fall problems?

Do Now:

A textbook and a metal sphere fall from the same height at the same time. Which one hits the ground first?

Gravity – the natural force of attraction in the universe

•Gravity causes objects to accelerate

•The acceleration due to gravity is a constant near the surface of the Earth for all objects

The elephant and penny hit the ground at the same time because the acceleration due to gravity is a constant

Demo: 2 pieces of paperDemo: 2 pieces of paper

What about crumbled and flat paper?

Demo

•Air resistance makes certain objects fall at different rates The elephant and

feather hit the ground at the different times because of air resistance

•What about in a vacuum (no air resistance)?

Demo•In a vacuum, all objects fall at the same rate

•If you travel high in the mountains or go to the moon, the acceleration due to gravity has a different constant

Apollo 15 VideoApollo 15 Video

Water Droplets with a Water Droplets with a Strobe lightStrobe light

http://www.youtube.com/watch?http://www.youtube.com/watch?v=rvY7NGncCgUv=rvY7NGncCgU

What’s Really HappeningWhat’s Really Happening

Time (s) Distance (m) Speed (m/s) Δd (m)

0 0.0 0.0 0.0

1 4.9 9.8 4.9

2 19.6 19.6 14.7

3 44.1 29.4 24.5

4 78.4 39.2 34.3

5 122.6 49.0 44.2

6 176.4 58.8 53.8

Free Fall Problems

With all free fall problems, we know two things immediately:

1.The object is dropped from rest

vi = 0 m/s

2. Acceleration is due to gravity

a = g = 9.8 m/s2

Solve the problem using the appropriate formula

Sample Problems

1.An object is dropped from a height of 2 m.

a. How long does it take to reach the ground?

Given

vi = 0 m/s

a = g = 9.8 m/s2

d = 2 m

t = ?

d = vit + ½at2

2 m = (0 m/s)t + ½(9.8 m/s2)t2

2 = 4.9t2 4.9 4.9

t2 = 0.4

t = 0.6 s

b. How fast is it moving when it hits the ground?

Givenvi = 0 m/sa = g = 9.8 m/s2

d = 2 mt = 0.6 svf = ?

vf = vi + atvf = 0 m/s + (9.8 m/s2)(0.6 s)vf = 5.9 m/s

2. An object falls off a bridge and takes 2.5 s to hit the water below.

a. How high is the bridge?

Given

vi = 0 m/s

a = g = 9.8 m/s2

t = 2.5 s

d = ?

d = vit + ½at2

d = (0 m/s)(2.5 s) + ½(9.8 m/s2)(2.5 s)2

d = 30.6 m

b. How fast is it moving when it hits the ground?

Givenvi = 0 m/sa = g = 9.8 m/s2

t = 2.5 sd = 30.6 mvf = ?

vf = vi + atvf = 0 m/s + (9.8 m/s2)(2.5 s)vf = 24.5 m/s

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