The position vector of a particle is given by $\overrightarrow{r}=\overrightarrow{r_0}\left(1–at\right)t$, where $t$ is time and $a$ as well as $\overrightarrow{r_0}$ are constant. After which time does the particle return to the starting point? What will be the velocity of the particle when it returns to the starting point? How much distance is covered by the particle in returning to the starting point?

Two particles $A$ and $B$ are projected from a building. $A$ is projected with speed $2V$ making an angle $30°$ with horizontal and $B$ with speed $V$ making an angle $60°$ with horizontal. Which particle will hit the ground earlier

A ball was thrown from height $H$ and the ball hit the floor with velocity $10\left(\hat{\mathrm{i}}–\hat{\mathrm{j}}\right)$ after $1.5 \sec$ of its projection. Find the initial speed of the ball.

A ball was thrown from height $H$ and the ball hit the floor with velocity $10\left(\hat{\mathrm{i}}–\hat{\mathrm{j}}\right)$ after $1.5 \sec$ of its projection. Find the angle of projection $\mathrm{\theta }$