$A$ person sitting in an open car moving at a constant velocity throws a ball vertically up into the air. The ball falls:

At a given instant of time, the position vector of a particle moving in a circle with a velocity $\vec{v} = 3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ is $\vec{r} = \hat{i} + 9 \hat{j} - 8 \hat{k}$. Its angular velocity $\vec{\omega}$ at that time is:

At a given instant of time,two particles have position vectors $4 \hat{i} + 4 \hat{j} + 57 \hat{k} \ m$ and $2 \hat{i} + 2 \hat{j} + 5 \hat{k} \ m$ respectively. If the velocity of the first particle is $0.4 \hat{i} \ ms^{-1}$,what is the velocity of the second particle in $ms^{-1}$ if they collide after $10 \ s$?

Two projectiles $A$ and $B$ are thrown with the same speed but at angles of $40^{\circ}$ and $50^{\circ}$ with the horizontal,respectively. Then:

The range of a projectile is $100 \ m$. Its kinetic energy will be maximum after covering a horizontal distance of: (in $m$)

If a person can throw a stone to a maximum height of $h$ meters vertically, then the maximum distance through which it can be thrown horizontally by the same person is