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 hiker stands on the edge of a cliff $$490 \mathrm{~m}$$ above the ground and throws a stone horizontally with an initial speed of $$15 \mathrm{~ms}^{-1}$$. The speed with which it hits the ground is

Two paper screens $$A$$ and $$B$$ are separated by $$150 \mathrm{~m}$$. A bullet pierces $$A$$ and than $$B$$. The hole in $$B$$ is $$15 \mathrm{~cm}$$ below the hole in $$A$$. If the bullet is travelling horizontally at the time of hitting $$A$$, then the velocity of the bullet at $$A$$ is $$\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$$