A particle moves in the plane xy with constant acceleration a directed along the negative y -axis. The equation of motion of the particle has the form y = p x - q x 2 where p and q are positive constants. Find the velocity of the particle at the origin of coordinates.

Question

A particle moves in the plane xy with constant acceleration a directed along the negative y -axis. The equation of motion of the particle has the form y = p x - q x 2 where p and q are positive constants. Find the velocity of the particle at the origin of coordinates., a 1 + p 2 2 q, a 1 + q 2 2 p, a 1 + q 2 p, a 1 + p 2 q

MARKS App · Accepted Answer

Comparing the given equation with the equation of a projectile motion, y = p x − q x 2 and y = x tan θ - gx 2 2 u 2 1 + tan 2 θ w e f i n d t h a t g = a , t a n θ = p a n d g 2 u 2 1 + tan 2 ⁡ θ = q ⇒ u 2 = g 2 q 1 + tan 2 ⁡ θ ⇒ u = a 2 q ( 1 + p 2 )

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