Question

У рыбака Василия есть новая двухместная резиновая лодка. Когда Василий садится в эту лодку один, она погружается в воду на треть своего объёма. Когда вместо Василия в лодку садится его приятель, она погружается на 3/8 своего объёма. Какова масса лодки? Какая часть объёма лодки будет погружена в воду, когда рыбаки сядут в лодку вместе? Масса Василия равна 75 кг, масса его приятеля — 90 кг.

Answer 1

1)
Вес Василия и лодки:
F = (75+X)*g     - здесь X - масса лодки      (1)
В этом случае сила Архимеда:
F = ρ*g (1/3)*V = (1000/3)*V *g                     (2)

Приравняем (2) и (1)
1000*V/3 = (75+X)      -  здесь g сократили.      (3)

Аналогично:

2)
Вес приятеля и лодки:
F = (90+X)*g     - здесь X - масса лодки      (4)
В этом случае сила Архимеда:
F = ρ*g (3/8)*V = (3000/8)*V *g                     (5)

Приравняем (5) и (4)
3000*V/8 = (90+X)      -  здесь g сократили.      (6)

3)
Решим систему уравнений  (3) и (6)
Получим:
1000*V = 225 + 3*X
3000*V = 720 +8*x
Отсюда:
X = 45 кг
V = 0,36 м³

4)

А если сядут вдвоем:
1000*k*V = (75+90+X)
360*k = 210
k = 210/360 = 21/36 = 7/12  объема.

Answer 2

Calculation of the Boat's Mass:

To determine the mass of the boat, we can use the information provided about its buoyancy when Vasily or his friend sit in it alone.

When Vasily sits alone in the boat, it sinks to one-third of its volume. When his friend sits in the boat instead of Vasily, it sinks to three-eighths of its volume.

Let's assume the total volume of the boat is V and its mass is M.

When Vasily sits alone in the boat, it sinks to one-third of its volume, which means that the volume of water displaced is V/3. According to Archimedes' principle, the buoyant force acting on the boat is equal to the weight of the water displaced. Therefore, the buoyant force is (V/3) * ρ * g, where ρ is the density of water and g is the acceleration due to gravity.

When Vasily's friend sits in the boat instead of Vasily, it sinks to three-eighths of its volume, which means that the volume of water displaced is 3V/8. Again, the buoyant force acting on the boat is equal to the weight of the water displaced. Therefore, the buoyant force is (3V/8) * ρ * g.

Since the buoyant force is equal to the weight of the boat, we can equate the two buoyant forces and solve for the mass of the boat:

(V/3) * ρ * g = (3V/8) * ρ * g

Simplifying the equation, we find:

8/3 = 3/8

Multiplying both sides of the equation by (3/8), we get:

1 = 1

This equation is true for any value of V and M. Therefore, we cannot determine the mass of the boat based on the information provided.

Calculation of the Submerged Volume when Both Fishermen are in the Boat:

To calculate the submerged volume when both Vasily and his friend are in the boat, we need to consider their combined weight.

The mass of Vasily is given as 75 kg, and the mass of his friend is given as 90 kg.

When both fishermen are in the boat, the boat sinks to a certain depth, and a certain volume of water is displaced. Let's assume this submerged volume is V_sub.

According to Archimedes' principle, the buoyant force acting on the boat when both fishermen are in it is equal to the weight of the water displaced. Therefore, the buoyant force is V_sub * ρ * g.

The total weight of Vasily and his friend is 75 kg + 90 kg = 165 kg. This weight is equal to the weight of the boat plus the buoyant force:

M * g + V_sub * ρ * g = 165 kg * g

Simplifying the equation, we find:

M + V_sub * ρ = 165 kg

Since we cannot determine the mass of the boat, we cannot calculate the submerged volume when both fishermen are in it based on the information provided.

In conclusion, based on the information given, we cannot determine the mass of the boat or the submerged volume when both fishermen are in it.