d = 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
• v_o does not equal 0

1. Velocity

v = v_o + at

2. Distance

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

v = v_o + at

2. Distance

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

2. 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

a = 0 v is constant d same (equal time intervals)

---

x

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

 

2. Vertical motion (falling object)

g = a = 10 m/s² v increase with time d increase with time

0s

1s

 

2s

 

 

3s

3. Combining Horizontal & Vertical Motion

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?

• The vertical motion is independent of the horizontal velocity.

• d (vertical ) = ½ at² d (horizontal) = v_ot

1. Hitting a target (projectile motion)

• Two important factors: