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A particle is projected with a velocity u at an angle α with the horizontal. Find the radius of curvature of the parabola traced out by the particle at the point where velocity makes an angle α/2 with the horizontal.

A particle is projected with a velocity u at an angle α with the horizontal. Find the radius of curvature of the parabola traced out by the particle at the point where velocity makes an angle α/2 with the horizontal.

Grade:12th pass

1 Answers

Arun
25750 Points
6 years ago
 
Radius of curvature for parabola is given as:

(1 + y’^2)^3/2/|y’’|........................(1)
 
Now the trajectory motion of the projectile motion i:

y = xtan(thetha) – gx^2/2u^2cos^2(thetha)
differentiate it both sides w.r.t x =>
 
dy/dx = tan(thetha) – gx/u^2cos^2(thetha)
SImilarly find double derivate and put both the eqns. in eqn. (1)
Put thetha ------> thetha/2
get the answer

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