Airplanes A and B are flying with constant velocity in the same vertical plane at angles $$30^\circ $$ and $$60^\circ $$ with respect to the horizontal respectively as shown in the figure. The speed of A is $$100\sqrt 3 $$ m/s. At time t = 0 s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A. If at t = t₀, A just escapes being hit by B, t₀ in seconds is

A rocket is moving in a gravity free space with a constant acceleration of 2 ms^–2 along + x direction (see figure). The length of a chamber inside the rocket is 4 m. A ball is thrown from the left end of the chamber in + x direction with a speed of 0.3 ms^–1 relative to the rocket. At the same time, another ball is thrown in - x direction with a speed of 0.2 ms^–1 from its right end relative to the rocket. The time in seconds when the two balls hit each other is

A train is moving along a straight line with a constant acceleration 'a'. A boy standing in the train throws a ball forward with a speed of 10 m/s, at an angle of $$60^\circ $$ to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball back at the initial height. The acceleration of the train, in m/s², is