Question

Капли дождя при скорости ветра v1=11 м/с падают под углом α=30 градусов к вертикали. При какой скорости ветра v2 капли будут падать под углом β=45 градусов?

Answer 1

Векторы u1 и u2 обозначим направление от капли до земли по вертикали. Считаем, что речь идёт о каплях на одной и той же высоте, то есть u1=u2=u. v1/u=tgα. v2/u=tgβ. Находим соотношение $\frac{v1}{tg \alpha } = \frac{v2}{tg \beta}$ Отсюда $v2= \frac{v1*tg \beta }{tg \alpha} = \frac{11*1}{ \frac{1}{ \sqrt{3} } } =11* \sqrt{3}= 19,053$ м/с. Поясняющий рисунок приведён во вложенном файле.

Ответ: 19,053 м/с.

Answer 2

Calculation of the Velocity of Raindrops at Angle β

To calculate the velocity of raindrops at angle β, we can use the given information about the velocity of raindrops at angle α and the angle between the vertical and the direction of motion of raindrops.

Given: - Velocity of raindrops at angle α (v1) = 11 m/s - Angle between the vertical and the direction of motion of raindrops at angle α (α) = 30 degrees - Angle between the vertical and the direction of motion of raindrops at angle β (β) = 45 degrees

We need to find the velocity of raindrops at angle β (v2).

To solve this problem, we can use the principle of conservation of energy. The kinetic energy of the raindrops at angle α should be equal to the kinetic energy of the raindrops at angle β.

The kinetic energy of an object can be calculated using the formula:

Kinetic Energy = (1/2) * mass * velocity^2

Since the mass of the raindrops is the same, we can equate the kinetic energies at angles α and β:

(1/2) * mass * v1^2 = (1/2) * mass * v2^2

Simplifying the equation, we get:

v1^2 = v2^2

Taking the square root of both sides, we find:

v1 = v2

Therefore, the velocity of the raindrops at angle β (v2) is equal to the velocity of the raindrops at angle α (v1), which is 11 m/s.

So, the raindrops will fall at angle β = 45 degrees with a velocity of v2 = 11 m/s.

Please note that the above calculation assumes ideal conditions and neglects factors such as air resistance, which may affect the actual behavior of raindrops.