Question

A particle is projected in xy plane with y axis along vertical, the point of projection is origin.The equation of the path is y=root 3 x-g/2x^2​.where y and x are in m.then the speed of projection in ms1

Answer 1

A particle is projected in xy plane with y axis along vertical, the point of projection is origin.

The equation of path is, $y=\sqrt{3}x-\frac{g}{2}x^2$ This is parabolic equation. hence question is based on projectile motion.

if a particle is projected with speed u at an angle α to the horizontal,

equation of path of the particle is given by, $y=xtan\alpha-\frac{g}{2u^2cos^2\alpha}x^2$

on comparing both equations we get,

tanα = √3 and 2u²cos²α = 2

tanα = √3 = tan60°

so, α = 60° => cosα= cos60° = 1/2

and now 2u²cos²α = 2

or, u² × (1/2)² = 1

or, u² = 1 × 4

or, u = 2

hence, speed of projection is 2m/s

Answer 2

Answer:

A particle is projected in xy plane with y axis along vertical, the point of projection is origin.

The equation of path is, y=\sqrt{3}x-\frac{g}{2}x^2y=

3

x−

2

g

x

2

This is parabolic equation. hence question is based on projectile motion.

if a particle is projected with speed u at an angle α to the horizontal,

equation of path of the particle is given by, y=xtan\alpha-\frac{g}{2u^2cos^2\alpha}x^2y=xtanα−

2u

2

cos

2

α

g

x

2

on comparing both equations we get,

tanα = √3 and 2u²cos²α = 2

tanα = √3 = tan60°

so, α = 60° => cosα= cos60° = 1/2

and now 2u²cos²α = 2

or, u² × (1/2)² = 1

or, u² = 1 × 4

or, u = 2

hence, speed of projection is 2m/s