A particle moves in the xy-plane with a constant acceleration g in the negative y-direction. Its equation of motion is y = ax - bx², where a and b are constants. Which of the following are correct?

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The x-component of its velocity is not constant.

At the origin, the y-component of its velocity is $2 a \sqrt{g / (2 b)} .$

At the origin, its velocity makes an angle $\tan^{- 1} a$ with the x-axis.

The particle does not moves like a projectile.

answer is C.

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Detailed Solution

A particle moves in the xy-plane with a constant acceleration g in the negative y-direction. Its equation of motion is y = ax - bx², where a and b are constant. Then the correct statements are
(i) The x-component of its velocity is constant.
(ii) At the origin, the y-component of its velocity is $a \sqrt{g / 2 b} .$
(iii) At the origin, its velocity makes an angle $\tan^{- 1} a$ with the x-axis.
(iv) The particle moves exactly like a projectile.