Math, asked by sushmitawangkheimayu, 10 hours ago

a particle is moving in a parabola with uniform angular velocity about the focus prove that it's normal acceleration at any point is proportional to the radius of curvature of its path at that point

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Answered by kshamika08

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Answered by kabyabhatt

Answer:

Y=album(sec(x)/a)Putting a =1Y=ln(sec(x))Slope of this curve,Tan(θ)=dy/dx=tan(x) ;equation(1)θ=xAngular velocity of tangent i.e. ω=dθ/dt=dx/dt=2Hence dx/dt=2By equation (1) dy/dt =tan(x) dx/dtHence velocity along y direction is 2 tan(x)So acceleration along y,= 2 sec(x) sec(x)At x=π/4, acceleration=2 √2 √2 =4

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a particle is moving in a parabola with uniform angular velocity about the focus prove that it's normal acceleration at any point is proportional to the radius of curvature of its path at that point​

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a particle is moving in a parabola with uniform angular velocity about the focus prove that it's normal acceleration at any point is proportional to the radius of curvature of its path at that point