A player kicks a foot ball at an angle \(30^{\circ}\) with the horizontal with an initial speed \(30 \mathrm{~ms}^{-1}\).
A second player standing at a distance of \(21 \sqrt{3} \mathrm{~m}\) 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 \(=10 \mathrm{~ms}^{-2}\) )

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.