Special Cases of Force. Projectile Motion. Projectile Motion. A projectile is any object which once a force is used to throw it, hit it , propel it in some fashion, no other force acts on the object except for gravity. Projection can be horizontal, with no initial vertical velocity
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If air resistance is negligible then only gravity
affects the path (trajectory) of a projectile.
The blue dot show the real motion
The path taken is the trajectory
This is horizontal projection
TimeVertical Velocity of Projectiles
For objects projected directly upward or projected at some angle above the ground, the vertical velocity must begin positive, decrease to zero, and then increase in the negative direction. (Remember, gravity is negative)
You can determine the displacement (range) of a projectile any any point along the trajectory.
X = horizontal distance (range)
vx = horizontal velocity
t = time
y = vertical displacement
vy = initial vertical velocity
g = acceleration due to gravity
t = time
projection is dependent on
the goal of the activity.
The angle that maximizes Range is = 45 degrees
70The effect of Projection velocity on the Range of a projectile
Origin xOrigin y
Positive x Positive y
xi = constant yi =
vxi = vyi =
ax = 0 ay = g
This is the only equation to use for the horizontal part of the motion
These 3 equations are for the vertical part of the motion
A zookeeper must throw a banana to a monkey hanging from the limb of a tree. The monkey has a habit of dropping from the tree the moment that the banana is thrown. If the monkey lets go of the tree the moment that the banana is thrown,will the banana hit the monkey?
Gravity free path
Gravity free path is “floating” at height of limb
Fall thru same heightWhen you take gravity into consideration you STILL aim at the monkey!
It works! Since both banana and monkey experience the same acceleration each will fall equal amounts below their gravity-free path. Thus, the banana hits the monkey.