Projectile motion

Projectile Motion

and

Free Fall vs Terminal Velocity

If James is holding a bullet at the same height Emily is holding a gun, and James drops the bullet at the same time Emily shoots the gun, which bullet will hit the ground first?

They will land at the same time!

Horizontal acceleration does not affect vertical acceleration.

Both bullets will accelerate vertically at 9.8m/s2

Projectile MotionProjectile Motion is the curved path an object

follows when thrown or propelled near the surface of the Earth.

It has two components:HorizontalVertical

…and they are independent of each other!

Does horizontal Motion affect Vertical Acceleration?

It doesn’t, it doesn’t, no seriously… IT DOESN’T!!!

Okay, enough about that…let’s “bite the bullet” and find out more about this problem…

I was there too, and I timed it: The bullets took two seconds to hit the ground.

What was their final speed in the vertical direction? and

What was their final speed in the horizontal direction if the initial speed in the vertical direction was 100m/s

(Let’s pretend they are in a magical place with no fluid friction)

For the horizontal…

100 meters per second, of course!

In the vertical…ΔV=gt

ΔV=(9.8m/s2)(2s)

ΔV=19.6m/s

9.8m/s 2

9.8m/s2

9.8m/s2

9.8m/s2

9.8m/s2

9.8m/s29.8m/s

2

9.8m/s 2

9.8m/s2

9.8m/s 2

9.8m/s2

What if Emily was holding the gun at an upwards angle so the path of the bullet looked like

INSTEAD OF

Would the bullet James dropped land first, or the bullet from Emily’s gun?

This time James’s bullet will land first.

By tilting the gun upwards, Emily gave the bullet an initial velocity in both the vertical and horizontal direction. Gravity will have to decelerate the bullet as it goes up before it pulls the bullet down to Earth.

If you were able to throw a ball really far (beyond the horizon)and really fast, would it ever hit the ground?

NO!Gravity would pull the ball down towards the

surface of the Earth, but since the Earth is curved, it is always bending away from the ball.

You could say the ball would be in orbit because it is in free fall and has horizontal velocity

Free-FallFree Fall occurs when the only force acting on

something is gravity.

Since outer space is a vacuum, there is no fluid friction acting on the ball- only gravity

Space Shuttle in Orbit

On Earth…Fluid friction prevents an object from being in free

fall on Earth.

As an object falls on Earth, the upward force of air resistance increases until it matches the downward force of gravity

When this happens, the net force is zero, acceleration stops, and the object falls at a constant velocity.

Terminal velocity is the constant velocity at which a falling object travels when the size of the upward force of air resistance matches the size of the downward force of gravity

Terminal VelocitiesPerson: can be between 53m/s and 76 m/s (or

119-170mph)

What factors can you think of that would change someone’s terminal velocity?

Terminal velocity depends on:Surface areaMass

Someone with a small surface area and a high mass will reach higher speeds than someone with a large surface area and small mass

It’s raining cats and dogs!Do cats really

have 9 lives?

Or do they have a nonfatal terminal velocity of 60mph because of their ability to “parachute” themselves?

1987 Study from Journal of American Veterinary Medical

AssociationStudied 132 cats

Up to 7 stories, injuries increased with height

At 7 stories and above, injuries sharply declined

After 5 stories of falling, cats reach terminal velocity

One cat survived a fall from 46 stories