Question

Two canoes are touching and at rest on a lake. The occupants push away from each other in opposite directions, giving canoe 1 a speed of 0.56 m/s and canoe 2 a speed of 0.45 m/s . If the mass of canoe 1 is 320 kg , what is the mass of canoe 2? Express your answer to two significant figures and include the appropriate units.

Answer 1

To solve this problem we will apply the concepts related to the conservation of momentum. Recall that the momentum is the product between the mass and the speed of the bodies. The mathematical expression for this problem could be given as

$m_1v_1 = m_2v_2$

Here,

$m_1$= Mass of canoe 1

$m_2$= Mass of canoe 2

$v_1$ = Velocity of canoe 1

$v_2$ = Velocity of canoe 2

Replacing with our values we have that,

$(320kg)(0.56m/s) = m_2(0.45m/s)$

$m_2 = \frac{(320kg)(0.56m/s)}{ (0.45m/s)}$

$m_2 = 3.9*10^2 kg$

Therefore the mass of the canoe 2 is 390kg.

NOTE: The omission of the negative speed symbol is given by the reference system and to facilitate the reading of the calculations.