A ball is thrown from the location (x_0, y_0 )=(0,0) of a horizontal playground with an initial speed v_0 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 (x_1, y_1 )=(L, 0). The stone is thrown at an angle (180- _1 ) from the

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A ball is thrown from the location (x_0, y_0 )=(0,0) of a horizontal playground with an initial speed v_0 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 (x_1, y_1 )=(L, 0). The stone is thrown at an angle (180- _1 ) from the +x-direction with a suitable initial speed. For a fixed v_0, when ( _0, _1 )= (45^ , 45^ ), the stone hits the ball after time T_1, and when ( _0, _1 )= (60^ , 30^ ), it hits the ball after time T_2. In such a case, (T_1 / T_2 )^2 is _______ .

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Correct answer: A. A

For case I : a_ rel =0 For collision v _0 2 = v 2 v = v _0 So T _1= L v _0 2 + v 2 _1= L 2 v _0 . .(1) For case II, a_ rel =0 For collision, v _0 3 2 = v 2 aligned & v = 3 v _0 \ & So, T _2= L v _0 2 + v 3 2 \ & ~T _2= L v _0 2 + 3 v _0 2 \ & T _2= L 2 v _0 . .(2) \ & so, ( T _1 ~T _2 )^2=( 2 )^2=2 ( T _1 ~T _2 )^2=2 aligned

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