2D Motion as 2 1D Motions

Q. A body is projected up with a speed $V$
along the line of greatest slope of an inclined plane of angle of inclination $\beta$. If the body collides elastically perpendicular to the inclined plane, find the time after which it crosses through its point of projection after collision ?

1. $\frac{2V}{g\left(\sin \beta \right)}$
2. $\frac{2V}{g\left(\tan \beta \right)}$
3. $\frac{2V}{g\left(\sqrt{1+3{\sin }^2\beta }\right)}$
4. $\frac{2V}{g\left(\sqrt{1+3{\tan }^2\beta }\right)}$

Q. Two guns situated on the top of a hill of height $10\text{m}$ fire one shot each with the same speed at some interval of time. One gun fires horizontally and other fires upward at an angle of ${60}^{\circ }$ with the horizontal. The shots collide in air at a point P. Then

1. the time-interval between the shots is 1 sec.
2. the time-interval between the shots is 2 sec.
3. the coordinates of the point P is $(5\sqrt{3},5)$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.
4. the coordinates of the point P is $(5,5\sqrt{3})$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.

Q. A 3 kg bomb explodes into 3 equal pieces A, B and C. A flies with a speed of 40 m/s and B with a speed off 30 m/s making an angle off ${90}^0$ with the direction of A. The angle made by the direction of C with that of A is

1. $co{s}^{-1}\left(\frac{4}{5}\right)$
2. $\pi -co{s}^{-1}\left(\frac{4}{5}\right)$
3. $co{s}^{-1}\left(\frac{3}{5}\right)$
4. $\pi -co{s}^{-1}\left(\frac{3}{5}\right)$

Q. Two guns situated on the top of a hill of height $10\text{m}$ fire one shot each with the same speed at some interval of time. One gun fires horizontally and other fires upward at an angle of ${60}^{\circ }$ with the horizontal. The shots collide in air at a point P. Then

1. the time-interval between the shots is 1 sec.
2. the time-interval between the shots is 2 sec.
3. the coordinates of the point P is $(5\sqrt{3},5)$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.
4. the coordinates of the point P is $(5,5\sqrt{3})$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.

Q. Two guns situated on the top of a hill of height $10\text{m}$ fire one shot each with the same speed at some interval of time. One gun fires horizontally and other fires upward at an angle of ${60}^{\circ }$ with the horizontal. The shots collide in air at a point P. Then

1. the time-interval between the shots is 1 sec.
2. the time-interval between the shots is 2 sec.
3. the coordinates of the point P is $(5\sqrt{3},5)$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.
4. the coordinates of the point P is $(5,5\sqrt{3})$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.

Q. Two guns situated on the top of a hill of height $10\text{m}$ fire one shot each with the same speed at some interval of time. One gun fires horizontally and other fires upward at an angle of ${60}^{\circ }$ with the horizontal. The shots collide in air at a point P. Then

1. the time-interval between the shots is 1 sec.
2. the time-interval between the shots is 2 sec.
3. the coordinates of the point P is $(5\sqrt{3},5)$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.
4. the coordinates of the point P is $(5,5\sqrt{3})$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.

Q. Two guns situated on the top of a hill of height $10\text{m}$ fire one shot each with the same speed at some interval of time. One gun fires horizontally and other fires upward at an angle of ${60}^{\circ }$ with the horizontal. The shots collide in air at a point P. Then

1. the time-interval between the shots is 1 sec.
2. the time-interval between the shots is 2 sec.
3. the coordinates of the point P is $(5\sqrt{3},5)$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.
4. the coordinates of the point P is $(5,5\sqrt{3})$ . Take origin of the coordinate system at the foot of the hill right below the muzzle and trajectories in $x–y$ plane.