Lecture 6: Vectors & Motion in 2 Dimensions (part II)

1. Lecture 6: Vectors & Motion in 2 Dimensions (part II)

2. Questions of Yesterday • 2) Two projectiles are thrown with the same initial speed, one at an angle q with respect to the ground and the other at an angle 90o - q. Both projectiles strike the ground at the same distance from the projection point. Are both projectiles in the air for the same length of time? • a) YES • b) NO • A heavy crate is dropped from a high-flying airplane as it flies directly over your shiny new car? Will your car get totaled? • YES b) NO

3. Relative Velocity Frame of Reference is important when measuring displacement, velocity & acceleration 60 mi/h Most reference frames are stationary with respect to earth Speed of moving object the same in any fixed reference frame What if your reference frame is moving?

4. 50 mi/h 60 mi/h Relative Velocity Frame of Reference is important when measuring displacement, velocity & acceleration Relative Velocity = Velocity of a moving object as measured by an observer in frame of reference Velocity of moving object relative to reference frame

5. 50 mi/h 60 mi/h Relative Velocity B C A vCB = vCA -vBA 0 mi/h vCA = velocity of C as measured by A = 60 mi/h vBA = velocity of B as measured by A = 50 mi/h vCB = velocity of C as measured by B = 10 mi/h

6. y rAE A Vector points TO Vector points FROM E x Relative Displacement in 2 Dimensions rAB = rAE -rBE A & B = moving objects/reference frames E = stationary reference frame with respect to Earth

7. rAB Relative Displacement in 2 Dimensions rAB = rAE -rBE y A rAE E x rBE B

8. y A rAE Dr Dt v = E x rBE B rAB Dt DtDt Relative Velocity in 2 Dimensions rAB = rAE -rBE DrAB = DrAE -DrBE vAB = vAE -vBE

9. Dr Dt v = vAB Dt DtDt Relative Velocity in 2 Dimensions rAB = rAE -rBE vAB = vAE -vBE vy A vAE DrAB = DrAE -DrBE E vx vBE B

10. vy vBA = -vAB vy A vAE A vAE vBA = -vAB E vAB E vx vx vBE B vBE B Relative Velocity in 2 Dimensions vBA = vBE -vAE vAB = vAE -vBE vBA = -(vAE -vBE)

11. Problem #1 An airplane that normally has a speed of 100 km/h through air is caught in a 100-km/h crosswind blowing from west to east, what will its velocity be relative to the ground when its nose is pointed north in the crosswind?

12. Problem #2 A canoe is paddled at 4 km/h directly across a river that flows 3 km/h. What is the resultant speed of the canoe? How fast and in what direction can the canoe be paddled to reach a destination directly across the river?

13. Problem #3 An airplane is flying horizontally with speed 1000 km/h (280 m/s) when an engine falls off. If it takes 30 s for the engine to hit the ground: How high is the airplane when the engine falls? How far horizontally does the engine travel while it falls? What is the engine’s velocity right before it hits the ground? If the airplane somehow continues to fly as if nothing had happened, where is the engine relative to the airplane at the moment the engine hits the ground? What is the engine’s velocity relative to the airplane?

14. Problem #4 A homerun is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from home plate. The ball is hit at an angle of 35o to the horizontal. Assume that the ball is hit at a height of 1.0 m above the ground. Find: the initial speed of the ball b) the time it takes the ball to reach the wall c) the velocity components and the speed of the ball when it reaches the wall

15. Questions of the Day A ball is thrown vertically upwards in the air by a passenger on a train moving with a constant velocity. To a stationary observer outside the train, is the velocity of the ball at the top of its trajectory a) greater than b) Less than c) Equal to the velocity observed by the passenger? 1) The hang-time of a basketball player who jumps a vertical distance of 2 ft is about 2/3 second. What will the hang-time be if the player reaches the same height while jumping 4 ft horizontally? a) less than 2/3 s b) greater than 2/3 s c) equal to 2/3 s