A particle moves in the plane XY with constant accelenration a direction along the negative Y-axis . The equation of motion of the particle has the form , `y = Ax - Bx^(2)`. Where A and B are positive constants. Find the velcotiy of the particle at the origin of the coordinates.

Explanation

Taking X-axis horizontal and Y-axis vertical.
We have , `Y = Ax - Bx^(2)`
Comparing with equation of trajectory ,
`y = x tan alpha - (gx^(2))/(2u^(2) cos^(2) alpha)`
` = x tan alpha - (gx^(2))/(2u) (1+tan^(2) alpha)`
We have `A = tan alpha ` and `B = (g)/(2u^(2)) (1+A^(2))`
(or)` u^(2) = ((1+A)^(2)g)/(2B) (or) u = sqrt(((1+A)^(2)g)/(2B))`