If two stones are projected at angles $\theta$ and $(90^{\circ}-\theta)$ respectively with the horizontal with a speed of $20 \ ms^{-1}$. If the second stone rises $10 \ m$ higher than the first stone,then the angle of projection $\theta$ is (acceleration due to gravity $g = 10 \ ms^{-2}$) (in $^{\circ}$)

$A$ player kicks a football at an angle of $30^{\circ}$ with the horizontal with an initial speed of $30 \,ms^{-1}$. $A$ second player, standing at a distance of $21 \sqrt{3} \,m$ from the first player in the direction of the kick, starts running to catch the ball at the same instant it is kicked. What is the minimum speed of the second player to catch the ball before it hits the ground? (Take acceleration due to gravity $g = 10 \,ms^{-2}$)

$A$ particle is moving with velocity $\vec v = K(y\hat i + x\hat j)$ where $K$ is a constant. The general equation for its path is

Two bodies of mass $10 \, kg$ and $5 \, kg$ are moving in concentric orbits of radii $R$ and $r$ such that their periods are the same. What is the ratio of their centripetal accelerations?

$A$ ball of mass $m$ is thrown vertically upward. Another ball of mass $2m$ is thrown at an angle $\theta$ with the vertical. Both the balls stay in the air for the same period of time. The ratio of the maximum heights attained by the two balls respectively is $\frac{1}{x}$. The value of $x$ is $.....$

$A$ ball is dropped from a height and falls due to gravity,while wind simultaneously imparts a uniform horizontal acceleration to it. Which one of the following figures best represents its path?