1© manhattan press (h.k.) ltd. 2.5 relative velocity

© Manhattan Press (H.K.) Ltd. 1

2.5 Relative velocity2.5 Relative velocity


Relative velocity

2.5 Relative velocity (SB p. 97)

Man in car moving at v:

In his observation, the ball moves in vertical path


Relative velocity


From stationary observer:

the ball moves along a parabolic path


Relative velocity


Relative velocity vBA

= Relative velocity of B relative to A

Go to

More to Know 4More to Know 4

vBA = vB - vA

Velocity of B relative to ground

Velocity of A relative to ground

Go to

Example 5Example 5



2.1 Displacement, velocity and acceleration 2.1 Displacement, velocity and acceleration in linear motionin linear motion1. 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.

tsv



2.1 Displacement, velocity and acceleration 2.1 Displacement, velocity and acceleration in linear motionin linear motion3. (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.

dtds

tsv

t

lim

o

dtdva



2.2 Motion graphs2.2 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.



2.3 Equations of uniformly accelerated 2.3 Equations of uniformly accelerated motionmotion8. For uniformly accelerated motion, the

following equations can be used:

(a) v = u + at

(b) s = ut + at2/2

(c) v2 = u2 + 2as



2.4 Motion under gravity2.4 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.



2.5 Relative velocity2.5 Relative velocity

10. Relative velocity is used to describe the motion between two objects moving with different velocities.

vBA = vB − vA

where vBA is the relative velocity of B relative to A,vB is the velocity of B (relative to ground),vA is the velocity of A (relative to ground).


End


Theory of special relativity

The equation vBA = vB – vA is valid for slow speeds

compared with the speed of light ( c = 3 × 108 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

TextText



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



Solution:Solution:Let vws be the relative velocity of wind relative to ship, vs be the velocity of ship and vw be the actual velocity of the wind.vws = vw – vs

vw = vws + vs

By drawing the vector diagram,

∴ The wind is actually blowing from N63.43°W towards the ship at 22.36 m s−1.

4363 1020tan

s m 36221020 122

.

.vw


Return to

TextText

1© manhattan press (h.k.) ltd. 2.5 relative velocity

Documents