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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