1© Manhattan Press (H.K.) Ltd. 2.5 Relative velocity

2 © Manhattan Press (H.K.) Ltd. Relative velocity 2.5 Relative velocity (SB p. 97) Man in car moving at v: In his observation, the ball moves in vertical path

3 © Manhattan Press (H.K.) Ltd. Relative velocity 2.5 Relative velocity (SB p. 97) From stationary observer: the ball moves along a parabolic path

4 © Manhattan Press (H.K.) Ltd. Relative velocity 2.5 Relative velocity (SB p. 97) Relative velocity v BA = Relative velocity of B relative to A Go to More to Know 4 More to Know 4 v BA = v B - v A Velocity of B relative to ground Velocity of A relative to ground Go to Example 5 Example 5

5 © Manhattan Press (H.K.) Ltd. 2.5 Relative velocity (SB p. 99) 2.1 Displacement, velocity and acceleration in linear motion 1. Distance is the total length of the actual path travelling by an object. It is a scalar. 2. Displacement (s) is the shortest length between the starting point and the end point of an object. It is a vector. 3. (a) Velocity (v) of an object is defined as the rate of change of displacement.

6 © Manhattan Press (H.K.) Ltd. 2.5 Relative velocity (SB p. 99) 2.1 Displacement, velocity and acceleration in linear motion 3. (b) The instantaneous velocity is given by: 4. Acceleration (a) is the rate of change of velocity. 5. A body is said to be moving under uniform acceleration if the magnitude of the acceleration is constant and along the same direction.

7 © Manhattan Press (H.K.) Ltd. 2.5 Relative velocity (SB p. 99) 2.2 Motion graphs 6. The velocity at any instant can be determined by finding the gradient of the displacement-time graph at that particular instant. 7. (a) The area under the velocity-time graph is the distance travelled. (b) The gradient of the graph is the instantaneous acceleration.

8 © Manhattan Press (H.K.) Ltd. 2.5 Relative velocity (SB p. 99) 2.3 Equations of uniformly accelerated motion 8.For uniformly accelerated motion, the following equations can be used: (a) v = u + at (b) s = ut + at 2 /2 (c) v 2 = u 2 + 2as

9 © Manhattan Press (H.K.) Ltd. 2.5 Relative velocity (SB p. 99) 2.4 Motion under gravity 9. If there is no resistance, all objects irrespective of mass, shape or size fall towards the earth with the same acceleration, the acceleration due to gravity (g). This motion is known as free fall.

10 © Manhattan Press (H.K.) Ltd. 2.5 Relative velocity (SB p. 99) 2.5 Relative velocity 10. Relative velocity is used to describe the motion between two objects moving with different velocities. v BA = v B − v A where v BA is the relative velocity of B relative to A, v B is the velocity of B (relative to ground), v A is the velocity of A (relative to ground).

11 © Manhattan Press (H.K.) Ltd. 2.5 Relative velocity (SB p. 100)

12 © Manhattan Press (H.K.) Ltd. End

13 © Manhattan Press (H.K.) Ltd. Theory of special relativity The equation v BA = v B – v A is valid for slow speeds compared with the speed of light ( c = 3 × 10 8 m s −1 ) only. For high energetic particles like electrons, their speed is about 0.9c and the above equation is not hold anymore. This can refer to the Einstein’s theory of special relativity. Return to Text 2.5 Relative velocity (SB p. 97)

14 © Manhattan Press (H.K.) Ltd. Q: Q: A ship is moving towards east with a velocity of 20 m s –1, the passengers on it feel that the wind is blowing towards them from the north with a velocity of 10 m s –1. What is the actual velocity of the wind? Solution 2.5 Relative velocity (SB p. 98)

15 © Manhattan Press (H.K.) Ltd. Solution: Solution: Let v ws be the relative velocity of wind relative to ship, v s be the velocity of ship and v w be the actual velocity of the wind. v ws = v w – v s v w = v ws + v s By drawing the vector diagram, ∴ The wind is actually blowing from N63.43°W towards the ship at m s − Relative velocity (SB p. 98) Return to Text