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 = mv2/r v (at that point) = u cos ѳ For the second situation: mg cos(ѳ/2) = mv’2/r v’ = vx + vy vx = 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: u2cos2 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?