Intro to Projectile on an Incline

Q. A particle is projected at an angle $\alpha$ with the horizontal from the foot of a plane, whose inclination to the horizontal is $\beta$. Find the velocity with which the particle strikes perpendicular to the inclined plane.

1. $u\cos (\alpha -\beta )$
2. $u\sin (\alpha -\beta )$
3. $u\sin \left(\frac{\alpha }{2}\right)$
4. $u\cos \left(\frac{\beta }{2}\right)$

Q. A particle is projected with certain velocity at an angle $\alpha$ above the horizontal from the foot of an inclined plane having inclination of ${30}^{\circ }$. If the particle strikes the plane normally then $\alpha$ is:

1. $\alpha ={30}^{\circ }+{\tan }^{-1}\frac{2}{\sqrt{3}}$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. $\alpha ={30}^{\circ }+{\tan }^{-1}\frac{\sqrt{3}}{2}$

Q. In figure the angle of inclination of the inclined plane is ${30}^{\circ }$. Find the horizontal velocity $V_0$ so that the particle hits the inclined plane perpendicularly.

1. $V_0=\sqrt{\frac{2gH}{5}}$
2. $V_0=\sqrt{\frac{2gH}{7}}$
3. $V_0=\sqrt{\frac{gH}{5}}$
4. $V_0=\sqrt{\frac{gH}{7}}$

Q. A particle is projected with certain velocity at an angle $\alpha$ above the horizontal from the foot of an inclined plane having inclination of ${30}^{\circ }$. If the particle strikes the plane normally then $\alpha$ is:

1. $\alpha ={30}^{\circ }+{\tan }^{-1}\frac{2}{\sqrt{3}}$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. $\alpha ={30}^{\circ }+{\tan }^{-1}\frac{\sqrt{3}}{2}$

Q.

A body thrown up along a frictionless inclined plane of angle of inclination ${30}^{\circ }$ covers a distance of 40 m along the plane. If the body id projected with the same speed at an angle of ${30}^{\circ }$ with the ground, it will have a range of
$(Takeg=10m{s}^{-2})$

1. 20 m

2. $20\sqrt{2}m$

3. $20\sqrt{3}m$

4. 40 m

Q. A particle is projected at an angle $\alpha$ with the horizontal from the foot of a plane, whose inclination to the horizontal is $\beta$. What is the value of $\tan (\alpha -\beta )$ if it strikes the plane at right angle?

1. $\frac{\cot \beta }{2}$
2. $\frac{\sin \beta }{2}$
3. $\frac{\tan \beta }{2}$
4. $\text{cosec}\beta$