Question

СРОЧНО 100 БАЛЛОВ ФАСТ ХЕЛП МИ Точечный источник света расположен на расстоянии 0,6 м от диска. Тень от диска падает на экран, который располагается на расстоянии 0,6 м от диска. Экран начинают медленно удалять от диска со скоростью 3 см/с. Через какое время площадь тени на экране увеличится в 2 раза?

Answer 1

2,2 м от диска из подобия треугольников

Answer 2

Task Analysis

To solve this problem, I need to calculate the time it takes for the shadow's area to double as the screen is moved away from the light source at a constant speed.

Given Information

- Distance from light source to disk (d1): 0.6 m - Distance from disk to screen (d2): 0.6 m - Speed of screen movement (v): 3 cm/s

Approach

To find the time it takes for the shadow's area to double, I will first calculate the initial area of the shadow on the screen. Then, I will determine the rate of change of the shadow's area with respect to time and use it to find the time it takes for the shadow's area to double.

Calculations

1. Initial Area of Shadow (A0): - The initial area of the shadow on the screen can be calculated using the similar triangles formed by the light source, disk, and screen.

2. Rate of Change of Shadow's Area (dA/dt): - I will calculate the rate of change of the shadow's area with respect to time using the concept of similar triangles and the given speed of the screen movement.

3. Time for Shadow's Area to Double (t): - Using the rate of change of the shadow's area, I will calculate the time it takes for the shadow's area to double.

Let's proceed with the calculations.