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A particle moves in the xy plane with a ...

A particle moves in the `xy` plane with a constant acceleration 'g' in the negative-direction. Its equqaiton of motion is `y = ax-bx^(2)`, where `a` and `b` are constants. Which of the following are correct?

A

The x-compound of its velocity is constant.

B

At the origin, the y-compound of its velocity is a `sqrt((g)/(2b))`.

C

At the origin, its velocity makes an angle `tan^(-1)` (a) with yeh x-axis.

D

The particle moves exactly like a projectile.

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`y = ax - bx^(2)`
Comparring with standard equaitons of
projectile `y = x tan theta -(1)/(2) (2X^(2))/(u^(2)cos^(2) theta)`
`tan theta = a rArr theta = tan^(-1)a, b = (g)/(2u^(2)cos^(2) theta)`
`u_(x) = sqrt((g)/(2b)) = constant rArr tan theta = (u_(y))/(u_(x))`
`rArr u_(y) u_(x) tan theta rArr u_(y) = a sqrt((g)/(2b))`
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