B M Sharma Solutions for Chapter: Kinematics II, Exercise 23: CONCEPT APPLICATION EXERCISE 5.2

A grasshopper can jump a maximum distance of $1.6 \mathrm{m}$. It spends negligible time on the ground. How far can it go in $10 \mathrm{s}$?

A projectile is thrown with an initial velocity of $\overrightarrow{v}=a\hat{\mathrm{i}}+b\hat{\mathrm{j}}$. If the range of a projectile is double the maximum height reached by it. Find the ratio $\frac{b}{a}$.

A ball is thrown at different angles with the same speed $u$ and from the same points and it has the same range in both cases. If $y_1$ and $y_2$ be the heights attained in the two cases, then find the value of $y_1+y_2$.

A particle $P$ is projected with the velocity $u_1$ at an angle of $30°$ with the horizontal. Another particle $Q$ is thrown vertically upwards with velocity $u_2$ from a point vertically below the highest point of the path of $P$. Determine the necessary condition for the two particles to collide at the highest point.

Two seconds after projection, a projectile is travelling in a direction inclined at $30°$ to horizontal. After one more second, it is travelling horizontally. Find the magnitude and direction of its velocity.

Two particles are separated at a horizontal distance $x$ as shown in the figure. They are projected at the same time as shown in the figure with different initial speeds. Find the time after which the horizontal distance between the particles becomes zero.

The horizontal range $\left(R\right)$ of a projectile becomes $\left(R+2H\right)$ from $R$ due to wind in the horizontal direction. Here, $H$ is the maximum height reached by the projectile. What constant horizontal acceleration is imparted by the wind.

A boy is running along the positive $x$-axis with $8 \mathrm{m} {\mathrm{s}}^{-1}$. While running he manages to throw a stone in a plane perpendicular to his direction of running with the velocity $12 \mathrm{m} {\mathrm{s}}^{-1}$ at an angle $30°$ with vertical. Find the speed of the stone at the highest point of the trajectory.