Two guns, mounted along the forward and rear directions of a moving railroad car, are firing at the same angle (relative to the car). The shells rise to a height of 500 m. The forward range of the shells is more than the backward gun's range by 200m. The speed of the railroad car is (take g = 10 m/s²)
Hint: The range is increased/decreased due to the movement of the car by V_car·T_shell.

1. 5 m/s

2. 10 m/s

3. 20 m/s

4. 40 m/s

                   
1. \(a\)
2. \(b\)
3. \(c\)
4. \(d\)

\({A}\) throws a ball towards \({B},\) who then catches it across the field. \({B}\) throws the ball back towards \({A},\) who then catches it. The angle of the throw is \(30^\circ\) for \({A},\) while it is \(60^\circ\) for \({B}'\text{s}\) throw. The ratio of their speeds of throw, \({v_A}: {v_B}\) is:
1. \(3\)

2. \(\dfrac13\)

3. \(\sqrt3\)

4. \(1\)

The average velocity component in the horizontal direction, for a projectile projected with an initial speed u, at an angle of \(\theta\) with the horizontal is v, when the average is calculated between the point of projection and the topmost point of the trajectory.
Then, the maximum height reached (H) is related to these quantities by

1. \(u^2=\frac{v^2}{2}+gH\)

2. \(u^2=\frac{v^2}{2}-gH\)

3. \(u^2=v^2+2gH\)

4. \(u^2=v^2-2gH\)