Falling Objects and Projectile Motion

Chapter 3

I) Acceleration due to Gravity

• g = 9.8 m/s = 10 m/s
• Valid only near the surface of the earth
• Gravitational acceleration does not depend on the weight of the object.
1. Falling objects
1. Dropping an object

* vo = 0 m/s g = a = 10 m/s2

1) Velocity

velocity => v = vo + at

2) Distance

distance (vo = 0)

d = ½ at2

distance (vo does not equal 0)

d = vot + ½ at2

t =0 s d = 0 m v = 0 m/s

t = 1 s d = 5 m v = 10 m/s

t = 2s d = 20m v = 20 m/s

t = 3s d = 45m v = 30 m/s

B) Throwing an object downward

• The object will reach the ground faster and with a greater velocity
• vo does not equal 0
1. Velocity
2. v = vo + at

3. Distance

d = vot + ½ at2

t = 0 d = 0 m v = 20 m/s

t = 1s d = 25m v = 30 m/s

t = 2s d = 60 m v = 40 m/s

t = 3s d = 105m v = 50 m/s

C) Throwing an object upward

• Gravity is ALWAYS downward
• When the ball leaves your hand, the primary force acting on it is gravity.
• Every second there is a change in velocity of 10 m/s
• At the tip of its flight, the velocity is zero.
1. Velocity
2. v = vo + at

3. Distance

d = vot + ½ at2

t = 2s v = 0m/s d = 20m

t = 1s v = 10m/s t = 3s v = -10m/s

d = 15m d = 15m

t = 0s v = 20m/s t = 4s v = -20m/s

d = 0 d = 0

1. Projectile Motion
• Trajectory => the path of an object thrown horizontally
• Trajectory has both a vertical and horizontal component to the motion.
• The vertical and horizontal motion are treated independently when calculating distance and velocity

v (horizontal)

v (vertical)

v (total)

A) Horizontal and Vertical Motion

1. Horizontal motion
2. a = 0 v is constant d same (equal time intervals)

x

0s 1s 2s 3s 4s 5s

3. Vertical motion (falling object)
4. g = a = 10 m/s2 v increase with time d increase with time

0s

1s

2s

3s

5. Combining Horizontal & Vertical Motion

Horizontal Velocity

Vertical Velocity

• As initial horizontal velocity increases, the horizontal distance increases.

1. Relationship of horizontal velocity and distance
• What determines the time of flight?
• Question: If three balls are launched at the same time with different horizontal velocities, which one will hit the floor first?

Answer: All will hit the floor at the same time.

All three balls are subjected to the same vertical

velocity (a = 10 m/s2)

• The vertical motion is independent of the horizontal velocity.
• d (vertical ) = ½ at2 d (horizontal) = vot

As the horizontal velocity increases, the horizontal distance increases

1. Hitting a target (projectile motion)
• Two important factors:

Initial velocity

Launch Angle