A projectile is thrown into space so as to have maximum horizontal range $R$. Taking the point of projection as origin, the coordinates of the points where the speed of the particle is minimum are-
$(R, R)$
$\left( {R,\frac{R}{2}} \right)$
$\left( {\frac{R}{2},\frac{R}{4}} \right)$
$\left( {R,\frac{R}{4}} \right)$
The $x-t$ graph of a particle moving along a straight line is shown in figure The distance-time graph of the particle is correctly shown by
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 eastwards with velocity of $5\,m/s$. In $10 \,sec$ the velocity changes to $5 \,m/s$ northwards. The average acceleration in this time is
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
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 $ ?