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 .
Answer
2
Solution
Both have acceleration g, so the relative velocity is constant. For a hit, vertical components must be equal: u 1 = v0 0.
Closing speed along x: v0 0 + u 1, so T = Lv0 0 + u 1.
(45 , 45 ): u = v0, closing speed = 2 v0 T1 = L 2v0.
(60 , 30 ): u = 3 v0, closing speed = v02 + 3v02 = 2v0 T2 = L2v0.
( T1T2 )2 = ( 2 2 )2 = 2
Answer: 2