A small steel ball $\mathrm{B}$ is at rest on the edge of a table of height $1\mathrm{m}$ . Another steel ball $\mathrm{A}$ used as the bob of a meter-long simple pendulum, is released from rest with pendulum suspension horizontal & swings against $\mathrm{B}$ as shown in figure. The masses of the balls are identical & collision is elastic. Considering motion of $\mathrm{B}$ only up until the moment it first hits the ground.

Two balls of mass $M$ and $2M$ are thrown horizontally with the same initial velocity $v_0$ from top of a tall tower and experience a drag force of $-kv\left(k>0\right)$ where $v$ is the instantaneous velocity.

Then,

Two posts of heights $20 \mathrm{m}$ and $10 \mathrm{m}$ are $60 \mathrm{m}$ apart, as shown in the figure. Foodgrains are continuously distributed between the two posts. A crow sitting on top of the taller post wants to pick up a grain and sit on the other post. What should be the distance of the grain it picks from the bottom of the taller post to minimise the total flight length?

The velocity of a projectile at the initial point $A$ is $\left(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}\right) \mathrm{m} {\mathrm{s}}^{-1}$. Its velocity (in $\mathrm{m} {\mathrm{s}}^{-1}$) at point $B$ is

A particle is projected with a velocity $v$ so that its range on a horizontal plane is twice the greatest height attained. Show that the range is $\frac{4v^2}{5g}$.

The correct answer is

Two particles are simultaneously projected in the horizontal direction from a point $P$ at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude $v$ each. The separation between the particles at a time when their position vectors (drawn from the point $P)$ are mutually perpendicular, is: