Motion in a Plane

A particle is thrown with a speed v from a point O at an angle with the horizontal plane such that it passes through the point P at a height of 1 m and horizontal distance of 5 m from O, as shown in the figure. If acceleration due to gravity is g ms-2, then the correct statement(s) is/are: [figure]

1. If = 45 , then v = 5 g2 ms-1.
2. If = 45 , the particle reaches its maximum height before it reaches P.
3. If = 30 , the particle reaches its maximum height after reaching P.
4. If = -1 ( 15 ), then v = 125 g ms-1.

A ball is thrown from the location (x0, y0) = (0, 0) of a horizontal playground with an initial speed v0 at an angle 0 from the +x-direction. The ball is to be hit by a stone, which is thrown at the same time from the location (x1, y1) = (L, 0). The stone is thrown at an angle (180 - 1) from the +x-direction with a suitable initial speed. For a fixed v0, when ( 0, 1) = (45 , 45 ), the stone hits the ball after time T1, and when ( 0, 1) = (60 , 30 ), it hits the ball after time T2. In such a case, (T1/T2)2 is .