A car travels with a speed of $$40 \mathrm{~km} \mathrm{~h}^{-1}$$. Rain drops are falling at a constant speed vertically. The traces of the rain on the side windows of the car make an angle of $$30^{\circ}$$ with the vertical. The magnitude of the velocity of the rain with respect to the car is

A projectile with speed $$50 \mathrm{~ms}^{-1}$$ is thrown at an angle of $$60^{\circ}$$ with the horizontal. The maximum height that can be reached is (acceleration due to gravity $$=10 \mathrm{~ms}^{-2}$$)

A boy throws a cricket ball from the boundary to the wicket keeper. If the frictional force due to air $$(f_a )$$ cannot be ignored, the forces acting on the ball at the position X are represented by

A particle of mass m is projected with a velocity u making an angle $$\theta$$ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height is