A projectile is launched from the ground, such that it hits a target on the ground which is 90 m away. The minimum velocity of projectile to hit the target is (acceleration due to gravity $$=10 \mathrm{~ms}^{-2}$$)

A force $$\mathbf{F}_1$$ of magnitude 4 N acts on an object of mass 1 kg , at origin in a direction $$30^{\circ}$$ above the positive $$X$$-axis. A second $$F_2$$ of magnitude 4 N acts on the same object in the direction of the positive $$Y$$-axis. The magnitude of the acceleration of the object is nearly.

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 $$=10 \mathrm{~ms}^{-2}$$)