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Wave Motion> A particle is projected in the xy plane w...

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A particle is projected in the xy plane with the x axis along vertical, the point of projection in orign . The equation of the path is y =root3 – g x ^2 divided by two where y and x are in meters . Then the speed of projection in ms^-1 is

a)2 B)root 3

c)4 d)root3 by 2

Adarsh Manoharan , 5 Years ago

Grade 11

2 Answers

Md Mushahid

Last Activity: 5 Years ago

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

the equation of the 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 $\alpha$ to the vertical equation of the path of the particle is given by $y =x\tan \alpha - \frac{g}{2u^{2}\times \cos ^{\alpha }}x^{2}$

on camparing the both equation we get

$\tan \alpha =\sqrt{3}$ and $2u^{2}\cos ^{2}\alpha =2$

$\alpha = \arctan \sqrt{3} =60\degree$

so, $\alpha = 60\degree$ $\Rightarrow$ $\cos \alpha = \cos 60\degree =\frac{1}{2}$

and now $2u^{2}\cos ^{2}\alpha =2$

$u^{2}\times\left ( \frac{1}{2} \right )^{2} =1$

$u^{2}=1\times 4$

$u=\sqrt{4}$

$u=2$

Hence, speed of projection is 2m/s

Khimraj

Last Activity: 5 Years ago

Trajectory of projectile motion when u is intial speed inclined Ф angle with horizontal
the equation of projectile is : y = xTanФ - gx²/ 2u²Cos²Ф

and the given equation is : y = √3x - gx²/2

on comparing both the equations ,we get

TanФ = √3

so, Ф = 60°
HENCE, the angle of projectile is 60°

and 2u²Cos²Ф = 2

so u²Cos²Ф = 1

u²cos²60° = 1

u²*(1/2)² = 1

u² = 2²

so, u = 2

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