Motion in two dimensions
- 1. TWO DIMENSIONAL MOTION MPHIRISENI NORMAN KHWANDA 5 March 2013
- 2. PRE-CONCEPT QUESTIONS 1. A projectile is fired into the air, and it follows the parabolic path as shown in the drawing
- 3. THE CONVERTIBLE CAR 2. Suppose you are driving in a convertible with the top down. The car is moving to the right with constant velocity as the diagram illustrates. You point a rifle upwards and fire it. In the absence of air resistance, where would the bullet land? A: Behind you (or the car) B: Ahead of the you (car) C: In the barrel of the riffle (back to where it was originally fired) The bullet moves with the same velocity horizontally as the car it only accelerates up and down due to gravity. The vertical and horizontal motions are independent of each other
- 4. THE CASE OF TWO BALLS 3. Ball 1 is thrown into the air and it follows the trajectory for a projectile motion shown in the drawing. At the instant Ball 1 is at the top, Ball 2 is dropped from rest from the same height, which ball reaches the ground first? A: Ball 1 reaches the ground first since it is moving while Ball 2 is stationery B: Ball 2 reaches the ground first because it has a shorter distance to travel C: Both balls reach the ground at the same time D: There is not enough information to tell which ball reaches the ground first Explanation: Both have zero velocity vertically and same height and under the gravitational acceleration g. hence they will reach at the same
- 5. THE PATH TAKEN BY THE BALL 4. The diagram represents a ball moving at a constant velocity of 50 m/s towards the right. Complete the path that the ball would take after reaching the edge B. Explanation: The ball will continue to move with the same velocity of 50 m/s horizontally but at the same time the force of gravity will be pulling the ball down immediately after leaving the edge, hence the parabolic path
- 6. MOTION IN TWO DIMENSIONS Summary: The motion is under the influence of gravity which always points towards the centre of the earth. The vertical and horizontal motions are independent from one another The motion horizontally remains constant (acceleration is zero) Air resistance is ignored The maximum velocity during free-fall depends on the initial velocity and initial position (height) Same height, same initial velocity implies same final velocity
- 7. EQUATIONS OF KINEMATICS HORIZONTALLY (ALONG THE X) vx vox axt x xo 1 vox vx t 2 2 2 v x v ox 2a x ( x xo ) 1 2 x xo voxt 2 axt
- 8. 3.2 EQUATIONS OF KINEMATICS VERTICALLY (ALONG THE Y) vy voy gt 1 2 y yo voyt 2 gt 1 y yo 2 voy vy t 2 2 v y v oy 2g ( y yo )
- 9. The x part of the motion occurs exactly as it would if the y part did not occur at all, and vice versa.
- 10. ASSUMPTIONS
- 11. EQUATIONS OF KINEMATICS FOR CONSTANT ACCELERATION IN TWO DIMENSIONAL MOTION
- 12. THE FINAL VELOCITY OF AN OBJECT
- 14. THE MAXIMUM HEIGHT H AND THE RANGE R
- 15. YOUR TURN
- 16. SOLUTION