Applications of Relative Projectile

Q.

The temperature of a hypothetical gas increases to $\sqrt{2}$ times when compressed adiabatically to half the volume. Its equation can be written as

1. 

2. 

3. 

4. 

Q.

A shell is projected from a gun with muzzle velocity $u$. The gun is fitted with a trolley car at an angle $\theta$ as shown in the fig. If the trolley car is made to move with constant velocity $v$ towards right, find the

(i) horizontal range of the shell relative to ground.

(ii) horizontal range of the shell relative to a person travelling with trolley.

1. ,

2. ,

3. ,

4. none of these

Q.

A shell is projected from a gun with muzzle velocity $u$. The gun is fitted with a trolley car at an angle $\theta$ as shown in the fig. If the trolley car is made to move with constant velocity $v$ towards right, find the

(i) horizontal range of the shell relative to ground.

(ii) horizontal range of the shell relative to a person travelling with trolley.

1. $\frac{2usin\theta (ucos\theta +u)}{g}$, $\frac{2usin\theta (ucos\theta -v)}{g}$

2. $\frac{u^{2}sin2\theta }{g}$, $\frac{u^{2}sin2\theta }{g}$

3. $\frac{2usin\theta (ucos\theta +v)}{g}$, $\frac{u^{2}sin2\theta }{g}$

4. none of these

Q. The horizontal range of a bullet fired at ${45}^{\circ }$ is $1000\text{m}$. If it is fired from the lorry, in the direction of lorry's motion, which is moving at $10\text{m/s}$, with the same velocity and elevation, then find its range in metre (Take $g=10{\text{m/s}}^2$)
Take $\sqrt{2}=1.414$.

Q. Two stones are projected simultaniously from a tower at different angles of projection with same speed $u$. The distance between two stones is increasing at constant rate $u$. Then the angle between the initial velocity vectors of the two stone is:

1. ${60}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${90}^{\circ }$