Relative Velocity | Presentation Slide

Each ray of light moves in the coordinate system 'at rest' with the definite, constant velocity V independent of whether this ray of light is emitted by a body at rest or a body in motion.

~ Albert Einstein

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E1.3 Relative Velocity (Rain falling vertically downward):

When a man is stationary and rain is falling vertically downward, the man has to held the umbrella vertically to save himself from the rain. The relative velocity of rain with respect to the man is in the vertical direction.
 

Suppose rain is falling vertically downward with velocity ($v_r$) and the man is walking in the horizontal direction with velocity ($v_m$), as shown in figure. 

The raindrops fall on him in the resultant direction with resultant velocity. This resultant velocity is inclined with vertical. 

Mathematically, 

$tan\theta = \frac{v_m}{v_r}$ 

Thus, a man walking in rain should hold his umbrella making an angle $\theta$ with the vertical, such that:

$\theta = tan^{-1}\frac{v_m}{v_r}$

To understand this concept is by directly solving the problem. 

A man is going due east with a velocity of $5 km/hr$. Rain falls vertically downwards at a speed of $10 km/hr$. Calculate the angle at which he should hold his umbrella so as to save himself from the rain? 

Answer: $26.56^0$  [Hence, the man has to hold his umbrella $26.56^0$ east of vertical.]

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E1.3 Kinematics (Relative Velocity):

The velocity of one body with respect to another body is called relative velocity.

Determination the Relative Velocity as follows:

I) When two objects are moving in the same direction:
When two bodies $A$ and $B$ are moving in the same direction with velocity $V_A$ and $V_B$ respectively. Then relative velocity of $A$ with respect to $B$ is:

$V_{AB} = V_A - V_B$ 

Also, the relative velocity of $B$ with respect to $A$ is:

$V_{BA} = V_B - V_A$ 

 

II) When two objects are moving in the opposite direction: 

When two bodies $A$ and $B$ are moving in the opposite direction with velocity $V_A$ and $V_B$ respectively. Then relative velocity of $A$ with respect to $B$ is:

$V_{AB}$ = $V_A - (-V_B)$ = $V_A + V_B$

 

III) When two bodies are moving inclined to each other: 

When two bodies $A$ and $B$ are moving with velocities $V_A$ and $V_B$ in different directions making an angle $\theta$. 

To find the velocity of B with respect to A, taking a velocity of A is reversed then taking $V_B$ and $-V_A$ as two sides of a parallelogram. The resultant gives the relative velocity as shown in figure.

(Similarly for relative velocity of A with respect to B).

Example: Rain falling vertically downward
                 Relative Velocity - ppt Slide

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