Projectile Motion



Projectile Motion

Launched Horizontally

An object launched horizontally will follow a parabola in flight. The result can be seen from the following falling object (the snapshots are taken at equal time intervals):

Note that the ball is in free fall vertically and moves at a constant speed horizontally since gravity only has a vertical component. We can solve projectile motion by treating the “x” and “y” directions independently. The equations of motion are greatly simplified using the following facts for an object launched horizontally:

o ax = 0

o ay = -9.8 m/s2

o Vy,i = 0

The equations in the y-direction become:

1) Vy,f = ay(t

2) Vy,f2 = 2ay(y

3) (y = (1/2)ay((t)2

And in the x-direction:

4) Vx = Vx,i = constant

5)(x = Vx(t

With this equations you can solve a variety of problems! (how far does it land, how much time does it take, final velocity, etc.)

Projectile Motion

Launched at an Angle

More generally, an object can be thrown with a nonzero vertical velocity (such as tossing a ball). Our everyday experience confirms that the object will follow a parabolic path:

Note that the object still follows a parabola because it is still in free fall vertically and moves at constant speed horizontally. However now we must include the initial velocity in the y-direction in the equations of motion. We can use the following facts to simplify them:

o ax = 0

o ay = -9.8 m/s2

The equations in the y-direction become:

1) Vy,f = Visin( + ay(t

2) Vy,f2 = Vi2(sin()2 + 2ay(y

3) (y = (Visin()(t + (1/2)ay((t)2

And in the x-direction:

4) Vx = Vx,i = Vicos( = constant

5) (x = (Vicos()(t

With this equations you can solve a great variety of problems and predict the motion of most falling objects!

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