Two projectiles P₁ and P₂ thrown with speed in the ratio $$\sqrt3$$ : $$\sqrt2$$, attain the same height during their motion. If P₂ is thrown at an angle of 60$$^\circ$$ with the horizontal, the angle of projection of P₁ with horizontal will be :

A person can throw a ball upto a maximum range of 100 m. How high above the ground he can throw the same ball?

A projectile is launched at an angle '$$\alpha$$' with the horizontal with a velocity 20 ms^$$-$$1. After 10 s, its inclination with horizontal is '$$\beta$$'. The value of tan$$\beta$$ will be : (g = 10 ms^$$-$$2).

A girl standing on road holds her umbrella at 45$$^\circ$$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of 15$$\sqrt2$$ kmh^$$-$$1, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is :