Solve the following :

Question:

What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle $0 / 2$ with the horizontal?

Solution:

Since acceleration in horizontal direction is zero

$u \cos \theta=\operatorname{vcos}\left(\frac{\theta}{2}\right)$

$v=\frac{u \cos \theta}{\cos _{\frac{\theta}{2}}^{\theta}}$

$\mathrm{a}_{\text {radial }}=\frac{V^{2}}{R}$

$R=\frac{\frac{w^{2} \cos ^{2} \theta}{\cos ^{2} \theta / 2}}{g \cos \theta / 2}$

$R=\frac{u^{2} \cos ^{2} \theta}{g \cos ^{3}(\theta / 2)}$

 

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