Question

С лодки массой 80 кг ныряет человек в горизонтальном направлении массой 60 кг. Скорость лодки 3 м/с. Какой станет скорость лодки после прыжка человека, если он прыгает с кормы со скоростью 2 м/с?

Answer 1

Решение на картинке.

Answer 2

Calculation of the Final Velocity of the Boat

To calculate the final velocity of the boat after the person jumps off, we can use the principle of conservation of momentum. According to this principle, the total momentum before the jump is equal to the total momentum after the jump.

The momentum of an object is given by the product of its mass and velocity. Therefore, the momentum of the boat before the jump is given by the product of its mass (80 kg) and velocity (3 m/s), and the momentum of the person before the jump is given by the product of their mass (60 kg) and velocity (0 m/s) since they are at rest on the boat.

Using the conservation of momentum, we can write the equation:

Initial momentum of the boat = Final momentum of the boat + Final momentum of the person

(80 kg) * (3 m/s) = (80 kg) * (final velocity of the boat) + (60 kg) * (final velocity of the person)

Simplifying the equation, we have:

240 kg·m/s = 80 kg * (final velocity of the boat) + 60 kg * (final velocity of the person)

Now, we need to determine the final velocity of the person after the jump. The person jumps off the boat with a velocity of 2 m/s in the opposite direction of the boat's motion. Therefore, the final velocity of the person is -2 m/s.

Substituting this value into the equation, we have:

240 kg·m/s = 80 kg * (final velocity of the boat) + 60 kg * (-2 m/s)

Simplifying further, we get:

240 kg·m/s = 80 kg * (final velocity of the boat) - 120 kg·m/s

Rearranging the equation to solve for the final velocity of the boat, we have:

80 kg * (final velocity of the boat) = 240 kg·m/s + 120 kg·m/s

80 kg * (final velocity of the boat) = 360 kg·m/s

Dividing both sides of the equation by 80 kg, we find:

Final velocity of the boat = 4.5 m/s

Therefore, the final velocity of the boat after the person jumps off will be 4.5 m/s.