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Question

with using formula of radius of curvature find the radius of curvature of projectile (4,8)at its higher point?

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Solution

Dear Student ,
Radius of curvature of any curved path, at any higher point on it, is given by:r=1+d2ydx232d2ydx2You can now use the expression of your trajectory. An alternate expression is:r=vx2-vy2axvy-vxaywhere vx and vy are the x and y components of velocity at some point and ax and ay are the x and y components of acceleration at the same point .Let an be the centripetal acceleration .So , an is the component of a perpendicular to v .an=a×vvan=axvy-vxayvx2+vy2Now , an=v2rso , r=v2anSubstitute vx2+vy2 for v2 and the above equation for an , you get ,r=vx2+vy232axvy-vxaySince we are using scalar notation here you could as well use ,r=vx2+vy232axvy-vxay

Regards

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