Question

Человек стоит на расстоянии 6 м от реки. На расстоянии 34 м от реки горит костер. Расстояние между перпендикулярами, опущенными на берег реки из точек, в которых находятся человек и костер, равно 30 м. Человек бежит со скоростью 5 м/с к реке, зачерпывает ведро воды, потом бежит к костру и заливает его. Какое минимальное время необходимо для этого, если на зачерпывание воды уходит 5 с?

Answer 1

Зеркально отразим положение человека относительно берега реки, для этого продлим перпендикуляр от человека вниз за линию берега, отложим на нем отрезок СN=CM, и соединим точки N и В. Прямая NB - краткий путь к костру (теоретически). А практически - человек должен идти по берегу. Найдем этот путь.

СМ:АВ=СО:ОА

Пусть ОС - х м

АО - (30-х)м

6/34=х/(30-х) 

(30-х)6=34х

180-6х=34х

40х=180

х=4,5(м) - ОС

ОM=√6²+4,5²=7,5(м)

ВО=√34²+(30-4,5)²=42,5(м)

ВN=BO+OM=42,5+7,5=50(м) - краткий путь к костру

t=S:V

50:5=10(с) - время движения человека к воде, затем к костру 

5 с необходимо, чтобы зачерпнуть ведро воды 

10+5=15(с) - минимальное время, необходимое человеку, чтобы залить костер.

Answer 2

Problem Analysis

We are given the following information: - A person is standing 6 meters away from a river. - There is a fire burning 34 meters away from the river. - The distance between the perpendiculars dropped from the person and the fire to the river bank is 30 meters. - The person runs towards the river at a speed of 5 m/s, fills a bucket with water, and then runs towards the fire to pour the water on it. - It takes 5 seconds to fill the bucket with water.

We need to determine the minimum time required for the person to complete this task.

Solution

To solve this problem, we can break it down into two parts: 1. The time it takes for the person to reach the river, fill the bucket, and return to the starting point. 2. The time it takes for the person to run from the starting point to the fire and pour the water on it.

Let's calculate each part separately.

Part 1: Reaching the River and Filling the Bucket

The person is running towards the river at a speed of 5 m/s. The distance between the person and the river is 6 meters. We can calculate the time it takes for the person to reach the river using the formula:

Time = Distance / Speed

Substituting the values, we get:

Time = 6 meters / 5 m/s = 1.2 seconds.

It takes an additional 5 seconds to fill the bucket with water.

Therefore, the total time for part 1 is:

Total Time for Part 1 = Time to reach the river + Time to fill the bucket = 1.2 seconds + 5 seconds = 6.2 seconds.

Part 2: Reaching the Fire and Pouring the Water

The distance between the person and the fire is 34 meters. The distance between the perpendiculars dropped from the person and the fire to the river bank is 30 meters. This forms a right-angled triangle.

Using the Pythagorean theorem, we can calculate the distance between the person and the fire along the river bank:

Distance along the river bank = √(Distance^2 - Perpendicular Distance^2)

Substituting the values, we get:

Distance along the river bank = √(34^2 - 30^2) = √(1156 - 900) = √256 = 16 meters.

The person is running at a speed of 5 m/s. We can calculate the time it takes for the person to reach the fire using the formula:

Time = Distance / Speed

Substituting the values, we get:

Time = 16 meters / 5 m/s = 3.2 seconds.

Therefore, the total time for part 2 is:

Total Time for Part 2 = Time to reach the fire = 3.2 seconds.

Total Time

The total time required for the person to complete the task is the sum of the times for part 1 and part 2:

Total Time = Total Time for Part 1 + Total Time for Part 2 = 6.2 seconds + 3.2 seconds = 9.4 seconds.

Therefore, the minimum time required for the person to complete the task is 9.4 seconds.

Please note that the calculations are based on the given information and assumptions made.