Two projectiles thrown at $$30^{\circ}$$ and $$45^{\circ}$$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :

A ball is projected from the ground with a speed 15 ms^$$-$$1 at an angle $$\theta$$ with horizontal so that its range and maximum height are equal,
then 'tan $$\theta$$' will be equal to :

At t = 0, truck, starting from rest, moves in the positive x-direction at uniform acceleration of 5 ms^$$-$$2. At t = 20 s, a ball is released from the top of the truck. The ball strikes the ground in 1 s after the release. The velocity of the ball, when it strikes the ground, will be :

(Given g = 10 ms^$$-$$2)

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 :