(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The first question:

‘A particle is projected with a speed u at an angle ѳ with the horizontal. Consider a small part of it’s path near the highest position and take it approximately to be a circular arc. What is the radius of this circle? This radius is called the radius of curvature of the curve at that point.’

The second question:

‘What is the radius of curvature of a parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle ѳ/2 with the horizontal?’

2. Relevant equations

For first situation: mg = mv^{2}/r

v (at that point) = u cos ѳ

For the second situation: mg cos(ѳ/2) = mv’^{2}/r

v’ = v_{x}+ v_{y}

v_{x}= u cos ѳ

3. The attempt at a solution

The first problem was easy to solve, because we could consider the velocity of the particle at the highest point, which was only u cos ѳ (as the vertical compnent was equal to zero) as v, and, solve using the formula for centripeal acceleration. My answer was: u^{2}cos^{2}ѳ/g

But, I’m having trouble with the second problem. How can Ifigure out the velocity of the particle at the position mentioned? I can’t figure out the vertical component at that point. Is there any formula or figuring out the velocity of a projrctile according to the angle it makes with the horizontal? Could you please help me solve this problem?

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# Homework Help: 'Centripetal Accelerations' and 'Radius of Curvatures' in Projectile Motion

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