1© manhattan press (h.k.) ltd. 2.5 relative velocity
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Relative velocity
2.5 Relative velocity (SB p. 97)
Man in car moving at v:
In his observation, the ball moves in vertical path
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Relative velocity
2.5 Relative velocity (SB p. 97)
From stationary observer:
the ball moves along a parabolic path
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Relative velocity
2.5 Relative velocity (SB p. 97)
Relative velocity vBA
= Relative velocity of B relative to A
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More to Know 4More to Know 4
vBA = vB - vA
Velocity of B relative to ground
Velocity of A relative to ground
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Example 5Example 5
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2.5 Relative velocity (SB p. 99)
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
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2.5 Relative velocity (SB p. 99)
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
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2.5 Relative velocity (SB p. 99)
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.
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2.5 Relative velocity (SB p. 99)
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
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2.5 Relative velocity (SB p. 99)
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.
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2.5 Relative velocity (SB p. 99)
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).
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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.
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2.5 Relative velocity (SB p. 97)
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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)
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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
2.5 Relative velocity (SB p. 98)
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