Question

С лодки, движущейся со скоростью 2 м/с, человек бросает весло массой 5 кг с горизонтальной скоростью 8 м/с в направление движению лодки. С какой скоростью стала двигаться лодка после броска, если ее масса вместе с массой человека равна 200 кг?​

Answer 1

m1=200 кг - масса лодки и человека

m2=5 кг - масса весла

v0=2 м/с - начальная скорость лодки, человека и весла

v2=-8 м/с - конечная скорость весла направлена противоположно лодке

v1- ? - конечная скорость лодки с человеком (уже без весла)

---------------

p0=(m1+m2)*v0 - импульс до броска

p1=m1*v1+m2*v2 - импульс после броска

по закону сохранения импульса po=p1

(m1+m2)*v0=m1*v1+m2*v2

m1*v1=(m1+m2)*v0-m2*v2=m1*v0+m2*(v0-v2)

v1=v0+(v0-v2)*m2/m1 = 2+(2-(-8))*5/200 м/с =

2,25 м/с - это ответ

Answer 2

Problem Analysis

We are given the following information: - The boat is moving with a velocity of 2 m/s. - A person throws an oar with a mass of 5 kg in the direction of the boat's motion with a velocity of 8 m/s. - The total mass of the boat and the person is 200 kg.

We need to find the final velocity of the boat after the oar is thrown.

Solution

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the oar is thrown is equal to the total momentum after the oar is thrown.

The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is defined as:

p = m * v

where p is the momentum, m is the mass, and v is the velocity.

Let's denote the initial velocity of the boat as V1, the final velocity of the boat as V2, the mass of the boat as M1, the mass of the person as M2, and the velocity of the oar as v.

Before the oar is thrown, the total momentum is the sum of the momentum of the boat and the momentum of the person:

Total momentum before = (M1 + M2) * V1

After the oar is thrown, the total momentum is the sum of the momentum of the boat (with the final velocity V2) and the momentum of the oar (with the velocity v):

Total momentum after = M1 * V2 + M2 * V2 + M2 * v

According to the conservation of momentum principle, the total momentum before and after the oar is thrown should be equal:

(M1 + M2) * V1 = M1 * V2 + M2 * V2 + M2 * v

We can rearrange this equation to solve for the final velocity of the boat (V2):

V2 = (M1 + M2) * V1 - M2 * v / (M1 + M2)

Now, let's substitute the given