Introduction to Projectile Motion

Horizontal and Vertical Motions of an Object Travelling at or Near Earth’s

Surface

Force and Projectiles

• When studying projectiles, we must consider all forces acting on the projectile.

• Objects at or near Earth’s surface are pulled downward by the force of gravity.

• For simplicity sake, we ignore the effects of air resistance on all projectiles.

• Thus the net force acting on the projectile is gravity.

Force of Gravity and Acceleration

• Since the force of gravity is the net force acting on the object, the object will accelerate with the acceleration due to gravity.

• All projectiles have the same acceleration:

Horizontal and Vertical Motions

• Since gravity acts to pull objects straight down (in the vertical direction only), only the vertical component of the projectiles motion is affected by this force.

• There are no forces acting on the horizontal components of the projectiles motion, thus horizontal motion is uniform.

Horizontal Component

• The horizontal component of a projectiles motion is uniform (i.e. constant velocity)

• The equation that is used to calculate constant velocity is:

t

dvav

Consider the Following Velocity Vector

θ

v

xv

yv

Determine the horizontal velocity vector in terms of the velocity vector and angle.

The Horizontal Velocity Equation

• The horizontal velocity can be determined using the following general equation:

Vertical Motion

• The vertical motion of a projectile is non-uniform (i.e. accelerated)

• The acceleration associated with the vertical motion of a projectile is the acceleration due to gravity

• All of the uniform acceleration equations studied this semester can be used to determine vertical motion of a projectile

Consider the Following Velocity Vector

θ

v

xv

yv

Determine the vertical velocity vector in terms of the velocity vector and angle.

The Vertical Motion Equations

• The vertical motion can be analyzed using the following equations:

Solving Projectile Problems

• Horizontal motion is always uniform.• Vertical acceleration always involves the

acceleration due to gravity.• When analyzing vertical motion, always

choose a positive direction (either up or down).

• The common variable between the two components is the time interval.

Steps

1. Determine the horizontal and vertical components of velocity.

2. Choose a positive direction in the vertical plane.

3. List all given data and any unknowns.4. Choose the appropriate equation(s).5. Solve.

Sample 1

• A girl runs off of a horizontal diving platform with a speed of 4.25 m/s. If the platform is 15.0 m above the surface of the water, how far horizontally from the edge of the diving platform does she hit the water? Ignore air resistance.

• With what velocity does she hit the water below?

Solutionvertical horizontal

Solutionvertical horizontal

Sample 2

• A golf ball is hit from a tee with an initial velocity of 25.0 m/s [30.0° above the horizontal]. It lands on a green at the same vertical height that it was hit from. Determine the horizontal distance that the ball travelled before hitting the green.

Solutionvertical horizontal

Solutionvertical

Try the following

• Page 46 Practice #3 and 5

• Page 50 Practice #9 and 10