Boat Momentum Transfer Scenario

What are the initial speeds of the boats v1 and v2 if the mass of boat 2 is m2 = 1 tonne?

Calculate the initial speeds of the boats based on the given scenario.

Answer:

The initial velocity of boat 1 (v1) is given by the formula: [tex]\\frac{7456 -8m_1}{m_1 + 907}[/tex]

The initial velocity of boat 2 (v2) is given by the formula: [tex]8 - ( \\frac{7456 -8m_1}{m_1 + 907})[/tex]

In the scenario provided, two rowboats are moving in opposite directions towards each other. When they are next to each other, a bag of mass m = 25 kg is transferred from boat 1 to boat 2. This results in boat 2 stopping its movement, while boat 1 continues moving with a speed v = 8 m/s.

The principle of conservation of linear momentum states that the total momentum of an isolated system is always conserved. By applying this principle, the initial velocities of the boats can be determined.

The initial velocity of each boat is calculated by using the formula: [tex]m_1 u_1 +m_2u_2 =m_ 1v_1 + m_2 v_2[/tex]

Let the mass of the first boat be m1 and the mass of the second boat be 907 kg. By solving the equations derived from the scenario, we can find the initial velocities of boat 1 and boat 2.

Initial velocity of boat 1 (v1): [tex]u_1 = \\frac{7456 -8m_1}{m_1 + 907}[/tex]

Initial velocity of boat 2 (v2): [tex]u_2 = 8 - (\\frac{7456 -8m_1}{m_1 + 907} )[/tex]

This scenario demonstrates the application of the conservation of linear momentum in determining the initial speeds of the two boats involved in the transfer of mass.