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A particle is projected up an incline plane of inclination x to the horizontal. If the particle strikes the plane horizontally then tanx is :

Anubhav kumar , 6 Years ago
Grade 11
anser 2 Answers
Venkat

Last Activity: 6 Years ago

Let the angle made by the  projectile with ground is \alpha
As the particle strikes the plane horizontally so its velocity is parallel to horizontal axis and vertical velocity is zero.
In vertical direction,
0=usin\alpha -gt \\ \\usin\alpha=g{\frac{2usin[\alpha -x]}{gcosx}} \\ \\cosxsin\alpha = 2(cosxsin\alpha -sinxcos\alpha) \\2sinxcos\alpha=cosxsin\alpha \\2tanx=tan\alpha \\tanx= 0.5*tan\alpha
 
 
 

Khimraj

Last Activity: 6 Years ago

verticle component of velocity will be zero.
and let angle made by projectile with ground is \Theta
THen
usin\Theta – gt =0
and time period t is given by 2usin(\Theta – x)/gcosx
THen
2sinxcos\Theta = cosxsin\Theta
so tanx = ½tan\Theta.
Hope it clears.
 

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