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# Motion in two dimensions

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### Motion in two dimensions

1. 1. TWO DIMENSIONAL MOTION MPHIRISENI NORMAN KHWANDA 5 March 2013
2. 2. PRE-CONCEPT QUESTIONS1. A projectile is fired into the air, and it follows theparabolic path as shown in the drawing
3. 3. THE CONVERTIBLE CAR2. Suppose you are driving in a convertible with the top down. Thecar is moving to the right with constant velocity as the diagramillustrates. You point a rifle upwards and fire it. In the absence ofair 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 itonly accelerates up and down due to gravity. The vertical andhorizontal motions are independent of each other
4. 4. THE CASE OF TWO BALLS3. Ball 1 is thrown into the air and it follows the trajectory for a projectilemotion shown in the drawing. At the instant Ball 1 is at the top, Ball 2 isdropped from rest from the same height, which ball reaches the groundfirst?A: Ball 1 reaches the ground first since it is moving while Ball 2 isstationeryB: Ball 2 reaches the ground first because it has a shorter distance totravelC: Both balls reach the ground at the same timeD: There is not enough information to tell which ball reaches the groundfirstExplanation:Both have zero velocity vertically and same height and under thegravitational acceleration g. hence they will reach at the same
5. 5. THE PATH TAKEN BY THE BALL4. The diagram represents a ball moving at a constant velocity of50 m/s towards the right. Complete the path that the ball wouldtake after reaching the edge B.Explanation:The ball will continue to move with the same velocity of 50 m/shorizontally but at the same time the force of gravity will bepulling the ball down immediately after leaving the edge, hencethe parabolic path
6. 6. MOTION IN TWO DIMENSIONSSummary: 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. 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. 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. 9. The x part of the motion occurs exactly as it would if they part did not occur at all, and vice versa.
10. 10. ASSUMPTIONS
11. 11. EQUATIONS OF KINEMATICS FOR CONSTANTACCELERATION IN TWO DIMENSIONAL MOTION
12. 12. THE FINAL VELOCITY OF AN OBJECT
13. 13. THE MAXIMUM HEIGHT H AND THE RANGE R