Projectile Motion on an Inclined Plane

A large heavy box is sliding without friction down a smooth plane of inclination $\text{θ}$. From a point $\mathrm{P}$ on the bottom of the box, a particle is projected inside the box. The initial speed of the particle with respect to the box is $u$ and the direction of projection makes an angle $\alpha$ with the bottom as shown in the figure:



Find the distance along the bottom of the box between the point of projection $\mathrm{P}$ and the point $\mathrm{Q}$ where the particle lands. [Assume that the particle does not hit any other surface of the box. Neglect air resistance]

A particle is projected up an inclined plane of inclination $\beta$ at an elevation $\alpha$ to the horizontal. Find the ratio between $\tan \alpha$ and $\tan \beta$, if the particle strikes the plane horizontally.
 

If $\alpha ={30}^o,\beta ={30}^o$ and $a=4.9m$, the initial velocity of projection is

If $\alpha ={30}^o,\beta ={30}^o$, the time of flight from $P$ to $Q$ is

Cotyledons are also called-

A particle is projected in air at an angle $\beta$ to a surface which itself is inclined at an angle $\alpha$ to the horizontal. Then distance $L$ is equal to –

An inclined plane is located at angle $\alpha =53°$ to the horizontal. There is a hole at point $\mathrm{B}$ in the inclined plane as shown in the figure. A particle is projected along the plane with speed $v_0$ at an angle $\beta =37°$ to the horizontal in such a way so that it gets into the hole. Neglect any type of friction. Find the speed $v_0$ (in $\mathrm{m} {\mathrm{s}}^{-1}$) if $h=1 \mathrm{m}$ and $l=8m$.

A particle P is projected at $t=0$ from point on the surface of a smooth inclined plane as shown in the figure simultaneously another particle Q is released on the smooth inclined plane from the same position. P and Q collide after $t=4$ seconds. Then choose the correct Option(s)

An inclined plane is making an angle $\beta$ with horizontal. A projectile is projected from the bottom of the plane with a speed u at an angle $\alpha$ with horizontal, then its range R when it strikes the inclined plane is:

An inclined plane making an angle $\beta$ with horizontal. A projectile projected from the bottom of the plane with a speed u at angle $\alpha$ with horizontal, then its maximum range $R_{max}$ is

A particle is projected from the ground and simultaneously a wedge starts moving towards the right, as shown in the figure. The maximum height of the wedge for which the particle will not hit the wedge is $\left[g=10 {\mathrm{ms}}^{-2}\right]$

On an inclined plane of inclination ${30}^{\mathrm{o}}$ , a ball is thrown at an angle of ${60}^{\mathrm{o}}$ with the horizontal from the foot of the incline with a velocity of $10\sqrt{3}\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$ . If $\mathrm{g}=10\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-2}$ , then the ball will hit the inclined plane in

A plane surface is inclined making an angle $\mathrm{\theta }$ with the horizontal. From the bottom of this inclined plane, a bullet is fired with velocity $\mathrm{\upsilon }$ . The maximum possible range of the bullet on the inclined plane is

A body is projected up a smooth inclined plane with velocity $v$ from the point $\mathrm{A}$ as shown in the figure. The angle of inclination is $45°$ and the top is connected to a well of diameter $40 \mathrm{m}$. If the body just manages to cross the well, what is the value of $v$? Length of the inclined plane is $20\sqrt{2}\mathrm{ }\mathrm{m}$.

Two bullets are fired simultaneously uphill parallel to an inclined plane. The bullets have different masses and different initial velocities. Which will strike the plane first?

The time taken by the projectile to reach from $A$ to $B$ is $t,$ then the distance $AB$ is equal to

A projectile is fired with a velocity $v$ at right angle to the slope which is inclined at an angle $\mathrm{\theta }$ with the horizontal. What is the range of flight?

A projectile is fired with a velocity $\mathrm{v}$ at right angle to the slope which is inclined at an angle θ$\mathrm{¸}$ with the horizontal. What is the range of flight?

Two bodies are projected from the same point with equal speeds in such directions that they both strike the same point on a plane whose inclination is β. If α be the angle of projection of the first body with the horizontal the ratio of their times of flight is

A particle is projected up an inclined plane with initial speed $v=20\mathrm{m}{\mathrm{s}}^{-1}$ at an angle $\theta =30°$ with plane. The component of its velocity perpendicular to plane when it strikes the plane is