Projectile Motion



Projectile Motion

We will consider a special case of two-dimensional motion when a particle moves in a vertical plane with some initial velocity (v0 ) but its acceleration is always the free-fall acceleration (g), which is downward. Such a motion is called a projectile motion.

In projectile motion, the horizontal motion and the vertical motion are independent of each other, that is, neither motion affects the other.

[pic]

The figure above shows the path of a projectile motion that is launched at x0 = 0 and y0 = 0, with the initial velocity v0 . As we can see, the horizontal velocity component remains constant but the vertical velocity component changes continuously.

See the video at

This video illustrates what is known as a “hippy jump”. Can you explain why the skateboarder lands back down on the skateboard after he jumps over his friend?

(NOTE: This was done by professional skateboarders. DO NOT try this at home!)

Below the figure illustrates the vertical motion where the projectile ball always hits the falling can. Each falls a distance (h) from where it would be if there were no free-fall acceleration.

[pic]

We will try this experiment in the lab. When the pellet leaves the gun G it activates a switch that disconnects the electromagnet M from electric current, allowing the can to fall. Can you and your classmates hit the falling can? Try hitting the can from when it is released from different heights. Does the pellet always hit the falling can?

If the experiment does not work sometimes can you explain why?

The equation of the path of the projectile after simplification will be:

y = (tan (0 )x - gx2 / 2(v0 cos (0 )2

Because (g), ((0 ), and (v0 ) are constants, the equation is of the form; y = ax + bx2 ,

which is the equation of parabola, so the path is parabolic.

[pic]

In the figure above (I) indicates the path of a fly ball, calculating by air resistance into account. (II) represents the path the ball would follow in a vacuum.

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download