Question

Капли дождя на окне неподвижного трамвая оставляют полосы наклоненные под углом 60° к вертикали. При движении трамвая со скоростью 10 м/с угол наклона полос уменьшается до величены 30°. Определить значение скорости капель дождя в безветренную погоду

Answer 1

Пусть:
 Vo - скорость капель в безветренную погоду;
 Vт - скорость трамвая;
 Vв - скорость ветра.
Сделаем чертежи.

Из первого чертежа:
tg 60° = Vв / Vo
Тогда:
Vв = √(3)*Vo

Из второго чертежа:
tg 30° = (Vв - Vт) / Vo = (√(3)*Vo - 10 ) / Vo = √(3) - 10 / Vo;
или
√(3) / 3 = √(3) - 10 / Vo;
10 / Vo = (2/3)*√(3) ;
10 / Vo ≈ 1,15;
Vo = 10/1,15 ≈ 8,7 м/с

Ответ: В безветренную погоду скорость падения капель приблизительно 8,7 метров в секунду

Answer 2

Problem Analysis

We are given that raindrops on the window of a stationary tram leave streaks inclined at an angle of 60° to the vertical. When the tram moves with a speed of 10 m/s, the angle of inclination of the streaks decreases to 30°. We need to determine the value of the raindrop speed in calm weather.

Solution

Let's assume that the raindrop speed in calm weather is represented by v.

When the tram is stationary, the angle of inclination of the streaks is 60°. According to the given information, the angle of inclination decreases to 30° when the tram moves with a speed of 10 m/s.

To solve this problem, we can use the concept of relative velocity. The angle of inclination of the streaks decreases because the raindrops are moving with a velocity equal to the tram's velocity in the opposite direction.

Using trigonometry, we can write the following equation:

tan(30°) = v / 10

Simplifying the equation, we have:

v = 10 * tan(30°)

Now, let's calculate the value of v.

Calculation

Using the given equation, we can calculate the value of v:

v = 10 * tan(30°)

Using a calculator, we find:

v ≈ 5.77 m/s

Therefore, the value of the raindrop speed in calm weather is approximately 5.77 m/s.

Answer

The value of the raindrop speed in calm weather is approximately 5.77 m/s.