Two boats on the water of the lake were motionless in relation to the water and were connected by a rope.

Two boats on the water of the lake were motionless in relation to the water and were connected by a rope. When the man in the first boat pulled the rope, the second boat began to move relative to the water with an acceleration of 0.2 m / s². What was the acceleration of the movement of the second boat relative to the first boat? The mass of the first boat is 200 kg, the mass of the second boat is 100 kg

a2 = 0.2 m / s2.

m1 = 200 kg.

m2 = 100 kg.

a1 -?

We express the acceleration of the first boat a1 from Newton’s second law: a1 = F21 / m1, where F21 is the force with which a person pulls the first boat from the second boat, m1 is the mass of the first boat.

According to Newton’s 3 laws, the force F21, with which the second boat acts on the first, is equal in magnitude and oppositely directed to the force F12, with which the first boat acts on the second: F21 = – F12.

F12 = a2 * m2.

The acceleration of the first boat a1 is found by the formula: a1 = a2 * m2 / m1.

a1 = 0.2 m / s2 * 100 kg / 200 kg = 0.1 m / s2.

Answer: the first boat will move with acceleration a1 = 0.1 m / s2.