Question

Тело брошено под углом 30° к горизонту со скоростью 20 м/с Чему равен радиус кривизны траектории в точке броска и верхней точке траектории?

Answer 1

Радиус кривизны траектории можно найти по формуле:

R = v^2 / (g * sin(2θ)),

где v - начальная скорость тела, g - ускорение свободного падения, θ - угол броска.

В данном случае, начальная скорость v = 20 м/с и угол броска θ = 30°. Ускорение свободного падения g примем равным 9,8 м/с^2.

Для точки броска (самого начала движения) подставим значения в формулу:

R1 = 20^2 / (9,8 * sin(2*30°)) ≈ 67,24 м.

Для верхней точки траектории (наивысшей точки движения) угол броска будет 90° - θ = 60°.

Подставим значения в формулу:

R2 = 20^2 / (9,8 * sin(2*60°)) ≈ 20 м.

Answer 2

Calculation of Radius of Curvature at the Point of Release

To calculate the radius of curvature at the point of release, we can use the formula:

R = v^2 / (g * sin(2θ))

where: - R is the radius of curvature - v is the initial velocity of the object - g is the acceleration due to gravity (approximately 9.8 m/s^2) - θ is the angle of projection (30° in this case)

Substituting the given values into the formula:

R = (20 m/s)^2 / (9.8 m/s^2 * sin(2 * 30°))

Calculating the value:

R ≈ 40.82 meters.

Calculation of Radius of Curvature at the Highest Point of the Trajectory

To calculate the radius of curvature at the highest point of the trajectory, we can use the same formula as above, but with the angle of projection being 90° (since the object reaches its highest point at this angle).

Substituting the given values into the formula:

R = (20 m/s)^2 / (9.8 m/s^2 * sin(2 * 90°))

Calculating the value:

R = ∞ (infinity)

At the highest point of the trajectory, the radius of curvature becomes infinite because the object momentarily comes to a stop before changing direction and starting to descend. Therefore, the curvature at this point is undefined.

In summary: - The radius of curvature at the point of release is approximately 40.82 meters. - The radius of curvature at the highest point of the trajectory is undefined (infinity).

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