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Projectile Motion

-An object thrown within an

initial velocity and acted upon by

the earth’s pull of gravity is

known as projectile.

-A projectile travels in a curved

path called trajectory.

-It is the motion of an object thrown or projected into the air, subjected

to only the acceleration of gravity.

• Projectile – object

• Trajectory – path

• The Independence of Motion

-Arrows represent the 

horizontal and vertical 

velocities at each position. 

Projectile- Any object which is projected by some means and continues to move due to its own inertia (mass).

• 2 Types of Projectile Motion:                                        

• Horizontal Projection

• Angular Projection

Two-dimensional motion of an object:

• Vertical

• Horizontal

• Types of Projectile Motion

Horizontal

• Motion of a ball rolling freely along a level surface

• Horizontal velocity is ALWAYS constant.

Vertical

• Motion of a freely falling object

• Force due to gravity

• Vertical component of velocity changes with time

• Combining the Components

-Together, these components produce what is called a trajectory or path.

-This path is parabolic in nature.

• Example of Projectile Motion

• Equations: Horizontal Projection

Kinematic Eqn. #2: d=Vit + gt²/ 2

• dy= gt²/ 2

• dx= Vx t

• Finding the Time and Vx:

Time= √2dy / g

Vx= dx / t

• Factors Affecting Projectile Motion

What two factors would affect projectile motion?

• Angle

• Initial Velocity

• Horizontally Launched Projectiles

Given: Vx= 100 m/s , dy= 500m, 

g= 9.8 m/s², t= 10.10s, dx= 1,010 m

Formula: dx= V x t

-Find the time: ( √2dy / g )

t= √2(500m) / 9.8 m/s²

t= √1,000 / 9.8 s²

t= √102.04 s²

t= 10.10 s

-Find the dx: ( dx = Vx t)

dx=  100 m/s (10.10s)  (cancel s)

dx= 1,010 m

• Equations: Angular Projection

• Time of flight: length of time 

t= 2Vi sinθ / g

• Range: maximum horizontal distance

R/dx= Vi² sin (2θ) / g

• Maximum height: maximum vertical distance

dy= (Vi sinθ)² / 2g

• Angularly Launched Projectiles

Given: Vi= 100 m/s, θ= 30°, g= 9.8 m/s²

1. t= 2(100m/s) sin (30°) / 9.8 m/s²

t= 200 m/s sin (30°) / 9.8 s²

t= 100/9.8 s²

t= 10.20s

2. R/dx= 100m/s² sin (2(30°) / 9.8 m/s² (cancel m/s²)

dx= 10,000 sin (30°) / 9.8

dx= 883.70 m

3. dy= [(100m/s) sin (30°)]² / 2(9.8m/s²)

dy= (50)² / 19.6

dy= 2,500 / 19.6

dy= 127.55 m

• Equation: Calculating Projection

• Range: maximum horizontal distance

R= Vi² sin (2θ) / g

sin 2θ = Rg / Vi²

Impulse and Momentum

• Linear Momentum

• Product of an object’s mass and linear velocity

• Symbol is p

• A vector 

quantity

• Kg m/s

• It is sometimes referred to as the inertia of a body in motion.

• Momentum is a latin word which means movement or moving power.

• P= as a symbol means progress.

• Used by the German scientist, Gottfried Wilhelm von Leibniz - He defined progress as the quantity of motion with which a body proceeds in a certain direction.

Formula: Finding the momentum - P=mv, Finding the mass - P/v = mv/v  Finding the velocity - P/m = mv/m

• Examples:

Given: m= 2500kg, v= 25 m/s

P= 2500kg (25 m/s)

P= 62,500 kg m/s

Given: m= 1200kg, P= 62,500 kg m/s

P/m = mv/m  (cancel m)          P/m = v 

v= p/m         v= 62,500 kg m/s / 1200kg

v= 52.08 m/s

• Impulse

• Product of force and the time during which the forces acts

• N*s or kg m/s

• The way a force changes the motion of a body depends on both magnitude of the force and how long the force acts.

• The stronger the force, the larger its effect.

• The longer the force acts, the greater is its effect

• Force varies inversely with the change in time. An increase in change in time means decrease in force.

Impulse - momentum relationship

• A bat hitting the baseball.

• The force exerted by the baseball on the bat multiplied by the time of contact between the ball and the bat is the impulse imparted to the ball.

Impulse is equal to the change in momentum.

• Formula

1. △p = F x t

2. △p = △mv

3. Ft = mv

Ft= m/s = △p

• Examples

Given- m= 0.05kg, v= 65 m/s

• Formula used:  △p = △mv

△p = 0.05kg (65m/s)

△p = 3.25 kg m/s