### Projectile Motion

Learn how to approach projectile motion questions using the main concepts when an object is in the air only under the influence of gravity.

Projectile motion results from an object being thrown, shot, rolling off a table, etc. and its in the air.  Once in the air, the only thing acting on the object is gravity.  The parabolic path the object takes is called the trajectory.

We use ideal conditions ignoring air resistance for this unit. Because Ideal means "perfect or simple" we may ignore other factors that could affect the situation.

### Independent X and Y axis Motion

The X and Y component of projectile motion are independent.  So no matter how fast or slow the horizontal component of velocity is, the Y axis does its own thing.  A bullet shot at 350 m/s from a height of 1 meter above the ground would fall at the same rate as a bullet dropped from the same height.  In the Y axis, both bullets start from rest, accelerating in a downward direction by 10 m/s2.  Therefore taking the same time to hit the ground.

### Projectile Motion Facts

X Axis Facts

• X axis motion is constant (look at the picture above: the blue arrow stays the same length representing constant velocity)
• If the horizontal velocity (vx) is 5 m/s at the beginning it as that same vx of 5 m/s everywhere.

Y Axis Facts

• Y axis motion is always accelerated down by 9.8 m/s2
• Acceleration of 9.8 m/s2 causes the object to slow on the way up and speed up when returning down
• At the top of the flight the Y axis velocity is 0 m/s but don't confuse this with acceleration still 9.8 m/s2 down
• If an object is caught at the same height, it's vertical velocity is the same magnitude as thrown but directed down

Overall Facts

• A projectile has maximum speed at the bottom of its flight
• A projectile has minimum speed at the top of its flight
• The top of a projectiles trajectory is composed of only horizontal velocity (vx)
• A projectile launched at a 45 degree angle will travel furthest downrange when landing at the same height (maximum X displacement).

### Relative Motion

Motion and many other things are relative.  Relativity in physics asks the question, "what is it compared to?"  You may think that you are sitting at a desk at rest but that is only relative to the surface of the earth.  Because the earth is rotating at 460 meters per second, relative to being in space, you're moving fast.

Use the concepts of constant horizontal velocity and accelerated vertical velocity to answer the questions.

### Example Questions

Q: How would a package dropped from a plane traveling at a constant horizontal velocity appear to the pilot?

A: The package and plane have the same vx so it appears to fall straight down.

Q: How would the package appear to an observer on the ground?

A: The observer would see the parabolic path the package actually takes to the ground.

Q: When would a package have to be dropped in order to hit a target?

A: You would have to drop the package before you get to the target.

### Projectile Motion Quiz

Projectile Motion Basics Quiz

Do you know your projectile motion facts?

Find out by taking our quiz

1 / 10

A ball is thrown horizontally at 20 meters per second and takes 1.3 second to hit the ground.  What happens to the time the object takes to fall if thrown much faster at 45 m/s?

2 / 10

What angle would you throw a ball to get the furthest X axis distance?

3 / 10

What angle would you throw a ball to get the greatest Y axis distance?

4 / 10

If a ball is thrown with a Y component of velocity of 30 m/s what is its Y component of velocity at the top of its flight path?

5 / 10

If a ball is thrown with a Y component of velocity of 30 m/s what is its acceleration at the top of its flight path?

6 / 10

If a ball is thrown with a Y component of velocity of 30 m/s what is the magnitude of Y component of velocity when it returns to the same height?

7 / 10

If a ball is thrown with a 7 m/s X component of velocity, what is the magnitude of X component velocity if still in the air after 1.3 seconds?

8 / 10

What is the actual speed of a ball is thrown with an X component velocity of 7 m/s forward and a Y component of velocity of 30 m/s up?

9 / 10

What is the actual speed of a ball is thrown with an X component velocity of 7 m/s forward and a Y component of velocity of 30 m/s up when at the top of it's flight path?

10 / 10

In the pilots perspective, how does a package dropped from a plane look like it falls? (Neglecting air resistance)