Intro to Projectile on an Incline

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 from horizontal making an angle ${60}^{\circ }$ with initial velocity 40 m/s. Find the time taken to the particle to make angle ${45}^{\circ }$ from horizontal.
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Q. There is a fire in the building which is started from its rooftop and is rapidly growing. Assuming that the water projected from hose behaves as a projectile, how far from that building should the fire hose be located to hit the highest possible height that it can hit. Given hose pipe is adjusted such that water leaves at a fixed angle with the horizontal at speed u m/s?

1. 

2. 

3. 

4. 

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 from a point at the foot of a fixed plane inclined at angle ${45}^{\circ }$ to the horizontal, in the vertical plane containing the line of greatest slope through the point. If $\theta (>{45}^{\circ }$) is the inclination to the horizontal of the initial direction of projection, for what values of $\tan \theta$ will the particle strike the plane horizontally?