T WO - DIMENSIONAL M OTION Physics Charles Lee

I NDEPENDENCE OF M OTION IN T WO D IMENSIONS When dealing with curved motion, horizontal and vertical motion are independent. Vertical velocity is constantly changing because of gravity. Horizontal velocity remains constant. Projectile motion - the curved motion of an object projected into the air projectile - an object fired into the air trajectory - the path of a projectile

S AMPLE P ROBLEM When solving problems, the horizontal and vertical velocities must be treated separately. An object is thrown horizontally at a velocity of 15m/s from a cliff 44m high. a. How long does it take the object to fall to the ground? b. How far from the base of the cliff will the object hit the ground?

S AMPLE P ROBLEM A movie director is shooting a scene which involves dropping a stunt dummy out of an airplane and into a swimming pool. The plane is 10.0m above the ground, traveling at a velocity of 22.5m/s in the positive x direction. The director wants to know where in the plane’s path the dummy should be dropped so that it will land in the pool.

P ROJECTILES F IRED AT AN A NGLE Even though a projectile may be fired at an angle, the velocities are still independent. The initial velocity must be resolved into horizontal and vertical components before solving the problem. Example: A motorcyclist plans to jump a canyon, 3.5km wide. A 30 0 ramp is constructed and an initial velocity of 196m/s is intended. Will he reach the other side?

P ROJECTILES L AUNCHED AT AN A NGLE Example: A zookeeper finds an escaped monkey hanging from a light pole. Aiming her tranquilizer gun at the monkey, the zookeeper kneels 10.0m from the light pole, which is 5.00m high. The tip of her gun is 1.00m above the ground. The monkey tries to trick the zookeeper by dropping a banana, then continues to hold onto the light pole. At the moment the monkey releases the banana, the zookeeper shoots. If the tranquilizer dart travels at 50.0m/s, will the dart hit the monkey or the banana?

3-4 R ELATIVE M OTION Observed motion depends on the frame of reference. A bus passes by at 45mph. Someone throws a baseball from the back to the front at 15mph. What is the speed of the baseball?

S AMPLE P ROBLEM A boat heading north crosses a wide river with a velocity of 10.00km/h relative to the water. The river has a uniform velocity of 5.00km/h due east. Determine the boat’s velocity with respect to an observer on shore.

E XPERIMENT : P APER T OWER You will be given the following material: 1 sheet of 8 X 10 paper 50cm of tape one ruler one pencil one pair scissors Purpose: Construct a tower of paper and tape of maximum height.