3-3 Projectile Motion
Two Dimensional Motion of Objects
 Projectile Motion – If air resistance is disregarded, projectiles
follow parabolic trajectories.
 Projectile - any object that the only force is gravity.
 Projectile Motion – free-fall with an initial horizontal velocity.
Baseball Projectile Motion
Horizontal and Vertical components – independent
of each other - both land at same time.
 Assuming no air resistance - Horizontal Velocity (Vx)
remains constant during entire path. The ball
moves the same horizontal distance in equal time
intervals.
 Velocity in the vertical direction (Vy) – changes by
9.8 m/s every second.
X and Y components of a velocity vector can simplify
projectile motion.
Observe Velocity Vectors:
Vertical component changes (by -9.8 m/s every second)
while Velocity in X direction remains constant
EQUATIONS
∆x = vx • t
Horizontal Launch
∆y = ½ g • t2
vy = g • t
t= √2 •∆y / g
t = Square root of 2 times the
vertical distance divided by g
vx = ∆x
t
Up and Down
∆y = ½ g • ( t/2 )2
vy = g • ( t/2 )
where t = total time
Projectiles Launched At An Angle
• Resolve the initial velocity into x and y components.
• The initial vertical velocity is the y component.
• The initial horizontal velocity is the x component.
Vx = Vx,i = vi cos θ = constant
Vy = Vi sin θ
Use Pythagorean theorem and inverse Tangent
function to find resultant and angle. (Vi)
Suppose a rescue airplane drops a relief package while it is
moving with a constant horizontal speed at an elevated height.
Assuming that air resistance is negligible, where will the relief
package land relative to the plane?
a. below the plane and behind it.
b. directly below the plane
c. below the plane and ahead of it
Suppose a rescue airplane drops a relief package while it is
moving with a constant horizontal speed at an elevated height.
Assuming that air resistance is negligible, where will the relief
package land relative to the plane?
a. below the plane and behind it.
b. directly below the plane
c. below the plane and ahead of it
If the monkey lets go of the tree the moment that the banana is fired, then where
should she aim the banana cannon?
a) Below the Monkey
b) Above the monkey
c) At the monkey
If the monkey lets go of the tree the moment that the banana is fired, then where
should she aim the banana cannon?
a) Below the Monkey
b) Above the monkey
c) At the monkey