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 at 2 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 2 nd 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/s 2 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