Relative Velocity of the Two Stones

To find the relative velocity of one stone with respect to the other stone, we need to consider the components of their velocities in the horizontal and vertical directions.

Given:
- The stones are projected with the same velocity V.
- One stone is projected at an angle of 30 degrees with respect to the horizontal.
- The other stone is projected at an angle of 60 degrees with respect to the horizontal.

Components of Velocity

Let's consider the stone projected at 30 degrees first. The horizontal component of its velocity can be calculated using the formula:

Horizontal component = V * cos(angle)

Since the angle is 30 degrees, the horizontal component of the velocity for this stone is:

Horizontal component = V * cos(30) = V * √3/2

Similarly, the vertical component of its velocity can be calculated using the formula:

Vertical component = V * sin(angle)

For this stone, the vertical component of the velocity is:

Vertical component = V * sin(30) = V * 1/2 = V/2

Now let's consider the stone projected at 60 degrees. Again, we can calculate its horizontal and vertical components of velocity using the same formulas.

Horizontal component = V * cos(angle)
Vertical component = V * sin(angle)

For this stone, the horizontal component of the velocity is:

Horizontal component = V * cos(60) = V * 1/2 = V/2

And the vertical component of the velocity is:

Vertical component = V * sin(60) = V * √3/2

Relative Velocity Calculation

To find the relative velocity of one stone with respect to the other stone, we subtract the corresponding components of their velocities.

Horizontal component of relative velocity = (V/2) - (V * √3/2) = -V * √3/2

Vertical component of relative velocity = (V * √3/2) - (V/2) = V * √3/2

The magnitude of the relative velocity can be found using the Pythagorean theorem:

Relative velocity = √[(Horizontal component)^2 + (Vertical component)^2]
= √[(V * √3/2)^2 + (-V * √3/2)^2]
= √[(3V^2/4) + (3V^2/4)]
= √[6V^2/4]
= √(3/2) * V
= √2 * V

Hence, the relative velocity of one stone with respect to the other stone is √2V.

As v know that in projectile.. the horizontal component. remains unchanged...so....use ...vcos30 = v cos 60..n then....vrelative = vleft+ vright as...direction are opposite...