An aircraft executes a horizontal loop with a speed of $150 \,m/s$ with its, wings banked at an angle of ${12^o }$. The radius of the loop is ..........  $km$. $(g = 10\,\,m/{s^2})$

A particle is moving on a circular path of radius $r$ with uniform velocity $v$. The change in velocity when the particle moves from $P$ to $Q$ is $(\angle POQ = {40^o})$

During which time interval is the particle described by these position graphs at rest?

ball is thrown from a point with a speed $‘v_0$’ at an elevation angle of $\theta $ . From the same point and at the same instant, a person starts running with a constant speed $\frac{{'{v_0}'}}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection $\theta $ ?

In projectile motion, the modulus of rate of change of velocity

A small body of mass $m$ slides down from the top of a hemisphere of radius $r$. The surface of block and hemisphere are frictionless. The height at which the body lose contact with the surface of the sphere is