Which type of mass movement involves the slow, downward progression of rock and soil down a low gradient slope?

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

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:

Shows that the projection angle ${\theta }_0$ for a projectile launched from the origin is given by

Lionel Messi is practising chip shots in his trailer. His aim is to kick the ball in such a way that it hits the target. He must kick the ball with a speed of 40m/s w.r.t. the trailer at all times.

Case 1:- His trailer moves with a constant velocity
Case 2:- The trailer rides off a cliff

The angle with the horizontal (from the frame of the trailer) at which Messi should kick the ball in Case 2 is

Show that for a projectile the angle between the velocity and the $x-$axis as a function of time is given by

$\theta \left(t\right)={\tan }^{-1}\left(\frac{v_{0y}-gt}{v_{0x}}\right)$

where the symbols have their usual meaning.