Applications of Relative Projectile

Q. A student is standing on a train travelling along a straight horizontal track at a speed of $10\text{m/s}$. The student throws a ball into the air along a path, that he sees to make an initial angle of ${60}^{\circ }$ with the horizontal along the track. The professor standing on the ground observes the ball to rise vertically, the maximum height reached by the ball is

Q. In the figure shown, the two projectiles are fired simultaneously. Find the minimum distance between them during their flight?

Q. A student is standing on a train travelling along a straight horizontal track at a speed of $10\text{m/s}$. The student throws a ball into the air along a path, that he sees to make an initial angle of ${60}^{\circ }$ with the horizontal along the track. The professor standing on the ground observes the ball to rise vertically, the maximum height reached by the ball is

Q. Suppose two particles, 1 and 2, are projected in vertical plane simultaneously.

Their angles of projection are ${30}^{\circ }$ and $\theta$ respectively with the horizontal. If they collide
after a time $t$ in air, then

1. $\theta ={\sin }^{-1}\left(\frac{4}{5}\right)$ and they will have same speed just before the collision.
2. $\theta ={\sin }^{-1}\left(\frac{4}{5}\right)$ and they will have different speed just before the collision.
3. $x<1280\sqrt{3}-960\text{m}$
4. it is possible that the particle collide when both of them are at their highest point.

Q. Two particles are projected simultaneously from the towers of same height as shown in the figure with velocities $V_A=20\text{m/s}$ and $V_B=10\text{m/s}$ respectively. They collide in air after 0.5 seconds. Find ${}^{\prime }{\theta }^{\prime }$. Answer in degrees

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. Two particles $A$ and $B$ are projected in air. $A$ is thrown with a speed of $60m/sec$ and $B$ with a speed of $80m/sec$ as shown in the figure.
What is the separation between them after $2sec$?

1. $100m$
2. $150m$
3. $200m$
4. $250m$

Q. Two particles $A$ and $B$ are projected in air. $A$ is thrown with a speed of $60m/sec$ and $B$ with a speed of $80m/sec$ as shown in the figure.
What is the separation between them after $2sec$?

1. $100m$
2. $150m$
3. $200m$
4. $250m$

Q. Projectile A is thrown horizontaly from tower of height H and projectile B is thrown from the ground at an angle $\theta$ as shown in the figure. During the duration when both are in air,

1. Path of A as seen by B will be a straight line
2. Path of A as seen by B will be a parabola
3. Motion of A is uniformly accelerated as seen by B.
4. Relative acceleration of A with respect to B is zero