B M Sharma Solutions for Chapter: Kinematics II, Exercise 44: CONCEPT APPLICATION EXERCISE 5.4

For a given velocity of projection from a point on the inclined plane, the maximum range down the plane is three times the maximum range up the incline. Then find the angle of inclination of the inclined plane.

A shell is fired from a gun from the bottom of a hill along its slop. The slope of the hill is $\alpha =30°$ and the angle of the barrel to the horizontal $\beta =60°$. The initial velocity $u$ of the shell is $21 \mathrm{m} {\mathrm{s}}^{-1}$, then find the distance of point from the gun at which the shell will fall.

The maximum range of rifle bullet on the horizontal ground is $6 \mathrm{km}$. Find its maximum range on an inclined of $30°$.

A bullet is fired from the bottom of the inclined plane at angle $\mathrm{\theta }=37°$ with the inclined plane. The angle of inclination is $30°$ with the horizontal. Find the position of the maximum height of the bullet from the inclined plane.

On an inclined plane, two particles $A$ and $B$ are projected with the same speed at the same angle with the horizontal, particle $A$ down and particle $B$ up the plane. If the ratio of time of flight of $A$ and $B$ is $\cot \left(\theta \right)$, where $\theta$ is the angle at which $B$ is projected measured from the inclined plane, find the angle at which particles are projected.

A particle is projected with velocity $u$ on an inclined plane at an angle $\mathrm{\theta }$ with the plane. If the particle lands on the plane at right angle, its time of flight is $\frac{u\mathrm{cosec}\mathrm{\theta }}{2g}$. Find the angle of inclination of the plane with horizontal.

A particle is projected on an inclined plane with a speed $u$ as shown in the figure. Find the range of the particle on the inclined plane.
  

There are three paths $a, b$ and $c$ of a projectile projected from point $P$ as shown in figure. Prove that $v_1>v_2$ and $v_3=v_4$. Which path is correct?