Goal: To projectile motions

Objectives:

1) To understand freefall motions in 1 D

2) To understand freefall motions in 2D

3) To understand air drag and terminal velocity

Freefall

• An object that falls with no force on it other than gravity is said to be in freefall

• While in freefall the effective “weight” is said to be zero as there is no normal force.

• The equations are used as normal and as seen in the previous lecture:

• Y = Yo + Vo t + ½ at2

• And V = Vo + at

Maximum height

• One thing to find is what the maximum height an object will reach.

• To do this you need to realize one concept, what will the vertical velocity be at the maximum height?

• Once you have that you can find the time it will take to reach that velocity using the

V = Vo + at equation

Example

• I throw a ball upwards.

• What the ball leaves my hand it is at a height of 2.0 m above the ground and traveling at a velocity of 20 m/s up.

• A) How much time will the ball take to reach its maximum height?

• B) What will the maximum height be?

Projectiles in 2 D

• Adding in the 2nd dimension isn’t as hard as you might think

• The two dimensions are separate.

• You now know how to do the vertical dimension.

• The horizontal is fairly straight forward once you understand what is happening.

First though

• I throw a ball with a purely horizontal velocity.

• What will the shape of its motion be?

Why?

• We know that the acceleration in the y direction is -9.8 m/s2 up

• What is the acceleration in the x direction?

So, for horizontal

• d = v t

• The trick is to find the time.

• To find the time you solve the vertical problem.

You try

• A cannon shoots a cannonball from the top of a hill

• The muzzle velocity of the cannon is 200 m/s forward.

• If the hill has a height of 50 m then how far will the cannonball fly before hitting the ground assuming we can ignore air resistance.

If time permits

• The cannon is shot at a 30 degree angle above the horizontal at 200 m/s from a 50 m tall hill.

• A) find the initial vertical and horizontal velocities of the cannon ball

• B) Find the time the cannonball will remain in the air.

• C) Find the horizontal distance the cannonball will travel in that time.

Air Drag

• So far we have ignored air resistance.

• As an object moves through the air the object runs into the air in front of it.

• This creates a drag.

• The amount of the air drag is proportional to the area of the object and the square of the velocity.

Terminal Velocity

• If an object is dropped from enough of a height eventually the air drag will have an effect.

• As the force of the air drag increases the downwards acceleration decreases.

• At some point the air drag force upwards (always opposes the motion just like friction) will equal the force of gravity.

• When this happens what will the net force be?

And so

• At terminal velocity an object will fall at a constant rate.

• However, if the area suddenly changes this will change the terminal velocity.

Conclusion

• We have learned about projectiles.

• We have learned about free fall without air drag

• We have learned about free fall with air drag and how it can lead to terminal velocity