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:

Consider the Following Velocity Vector θ 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 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 Determine the horizontal and vertical components of velocity. Choose a positive direction in the vertical plane. List all given data and any unknowns. Choose the appropriate equation(s). 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?

Solution vertical horizontal

Solution vertical 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.

Solution vertical horizontal

Solution vertical

Try the following Page 46 Practice #3 and 5 Page 50 Practice #9 and 10