So, that's why they love cricket

Classical Mechanics Level 3

In a cricket match, a pace bowler \(2\text{ m}\) tall throws a yorker ball with a horizontal velocity of \(20\text{ m/s}\). The batsmen hits the ball with twice the horizontal velocity thrown by the bowler at an angle of \({45}^\circ\) with the horizontal. The ball lands just in front of a fielder who kicked the ball with his foot at an angle of \({30}^\circ\) with the horizontal in such a way that it landed just in front of the foot of the bowler. Find the velocity with which the fielder kicked the ball.

Details and assumptions:

  • Assume the air friction to be negligible.
  • Assume that the position of the batsman, bowler and fielder are collinear and the batsman hits the ball in the collinear line.
  • Assume that the bowler throws the ball by stretching his hand just above the top of his head.
  • Assume that the bowler does not move fom his position after releasing the ball from the crease line.
  • Take \(g\) (acceleration due to gravity) as \(10{\text{m/s}}^2\).
  • Round your answer (in \(\text{m/s}\)) off to the nearest integer.

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