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-
$(R, R)$
$\left( {R,\frac{R}{2}} \right)$
$\left( {\frac{R}{2},\frac{R}{4}} \right)$
$\left( {R,\frac{R}{4}} \right)$
A body slides down a frictionless track which ends in a circular loop of diameter $D$, then the minimum height $h$ of the body in term of $D$ so that it may just complete the loop, is
Two cars of masses $m_1$ & $m_2$ are moving along the circular paths of radius $r_1$ & $r_2$ respectively. Their speeds are such that they complete one round in same time. The ratio of angular speeds of two cars is
The $x-t$ graph of a particle moving along a straight line is shown in figure The $a-t$ graph of the particle is correctly shown by
If the instantaneous velocity of a particle projected as shown in figure is given by $v =a \hat{ i }+(b-c t) \hat{ j }$, where $a, b$, and $c$ are positive constants, the range on the horizontal plane will be
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 $ ?