# Problem №1 (10 points)

A stone is thrown from the surface of the Earth at an angle of $60^{\circ}$ to the horizon with an initial velocity $v_{0}=10 \mathrm{~m} / \mathrm{s}$. Determine the radius of curvature of the trajectory at the final point of the flight. The acceleration due to gravity $g=10 \mathrm{~m} / \mathrm{s}^{2}$.

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# Solution:

The final velocity of the stone is equal to its initial velocity:

![](https://cdn.mathpix.com/cropped/2024_05_06_43bee554500cb324c5d0g-05.jpg?height=568&width=691&top_left_y=1104&top_left_x=91)

The centripetal acceleration at the final point of the flight:

$a_{\text{c}}=g \cdot \cos 60^{\circ}=5 \mathrm{~m} / \mathrm{s}^{2}$

The radius of curvature of the trajectory at the final point of the flight:

$R=\frac{v^{2}}{a_{\text{c}}}=\frac{10^{2}}{5}=20 \mathrm{~m}$

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