Applications relative to motion concept

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# Applications relative to motion concept

In this case, the three velocities with which we have to deal are:

Velocity of rain wrt ground;

Velocity of man wrt ground;

Velocity of rain wrt man From relative motion equation,

From this equation, we can construct a velocity vector diagram, which would be very helpful in solving the question.

The velocity vector diagram for a particular situation is shown in figure.

From sine law

Remember!

are not representing the length of triangles.

If in-air problems wind is blowing, then consider also the effect of wind blowing in the application.

## River Problems

In this case, we have to deal with the following velocities:

Velocity of swimmer/steamer/boat wrt river/water/stream.

The velocity of swimmer/steamer/boat wrt ground.

From relative motion

For the situation shown in figure, a boat is crossing the river and it is heading (moving) along AP as shown,

then the time taken by boat to cross the river is,

and it will reach point Q due to river flow

The distance

is termed as drift.

The velocity of plane wrt ground.

The relative motion equation would be

## Aeroplane Problems

Here the following velocities are to be analyzed:

The velocity of plane wrt air.

The velocity of air wrt ground.

Conditions for Collision of Two Projectiles from Different Heights

Consider that two particles are projected from A and B with initial speed u1 and u2, respectively as shown in figure.

As the relative acceleration of 1 wrt 2 is zero, so particles will collide only and only 1 velocity of 1 wrt 2 would be along line AB. v12x = Component of velocity of 1 wrt 2 along X axis = u1

u12y = Component of velocity of 1 wrt 2 along Y axis = u1 sin ∝ 1  + u2 sin ∝2

Let velocity of 1 wrt 2 is making an angle β with +ve X-axis,
then

For collisions to take place, θ = β

### Path of projectile as seen from another projectile

Consider two particles A and B projected from the same point with initial speed u1 and u2 respectively as shown in figure.

So, the motion of one projectile as seen from another projectile will be a straight line.

Multiple Choice Questions