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JEE MainPhysicsMotion in Two Dimensions

A water sprinkler placed on the ground sprays water in all directions with a constant speed. The maximum circular area covered by the water on the ground is 144 m ^2 . If the nozzle of the sprinkler is pointed vertically upwards, the maximum height the water jet can reach is

Options

  1. A12 m
  2. B24 m
  3. C3 m
  4. D6 m

Correct answer

D. 6 m

Step-by-step solution

The maximum horizontal range R_ max determines the radius of the circular area covered on the ground. Area A = R_ max ^2 144 = R_ max ^2 R_ max = 12 m We know that maximum horizontal range is given by R_ max = v^2 g . The maximum vertical height reached when projected straight up is H_ max = v^2 2g . Therefore, H_ max = R_ max 2 = 12 2 = 6 m . Answer: 6 m

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