A player kicks a foot ball at an angle 30^ with the horizontal with an initial speed 30 ~ms ⁻¹ . A second player standing at a distance of 21 3 ~m from the first and in the direction of kick. Starts running to catch the ball, at the same instant as kicked by first player. The minimum speed of second player to catch the ball before it hits the ground is (Take, acceleration due to gravity =10 ~ms ⁻² )

Step-by-step solution

The motion of the ball is shown below. Range, aligned R & = u^2 2 g & = 900 (2 30) 10 = 900 60^ 10 R & = 900 3 10 2 = 900 3 20 =45 3 ~m aligned Since, the IInd player is at 21 3 ~m in the direction of kick and he is running to catch the ball, so this can be represented as shown Let the man runs with speed v towards point P to catch the ball just at point P before it touches the ground in the same time when ball reaches the point P . The man will travel distance =24 3 ~m Distance = speed time 2 u 3 =v t Where, t is