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AP EAMCET20224 Jul 2022Evening ShiftPhysicsMotion in Two DimensionsActual

y = P t 2 - Q t 3 m is the vertical displacement of a ball which is moving in vertical plane. Then the maximum height that the ball can reach is,

Options

  1. A27 P 3 4 Q 2
  2. B4 Q 2 27 P 3
  3. C4 P 3 27 Q 2
  4. D27 Q 2 4 P 3

Correct answer

C. 4 P 3 27 Q 2

Step-by-step solution

Velocity is written as the rate of change of displacement. v y = d y d t = d P t 2 - Q t 3 d t = 2 P t - 3 Q t 2 At maximum height, the velocity of the particle will be zero. Therefore, t ( 2 P - 3 Q t ) = 0 ⇒ t = 0   &   2 P 3 Q Considering t = 2 P 3 Q as t = 0 means begining of motion. Now maximum height will be, y = P t 2 - Q t 3 = P 2 P 3 Q 2 - Q 2 P 3 Q 3 = 2 P 3 Q 2 P - 2 P 3 = 4 P 3 27 Q 2

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