two campers dock a canoe. one camper steps onto the dock. this camper has a mass of 80 kg and moves forward at 4 m/s. with what speed and direction do the canoe and the other move if their combined mass is 110 kg?

the answer is 2.9

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To find the speed and direction of the canoe and the other camper, we need to apply the law of conservation of momentum. According to this law, the total momentum before an event is equal to the total momentum after the event, provided that no external forces are acting on the system.

Here, the momentum of an object is given by the product of its mass and velocity. Let's designate the velocity of the canoe as v1 and the velocity of the other camper as v2. Since both velocities are dependent on the mass of the system, we'll use the subscripts "1" and "2" to denote the respective masses and velocities.

Initial momentum = Final momentum

Before the event:
Initial momentum of camper = mass of camper * velocity of camper (m1v1)
Initial momentum of canoe = mass of canoe * velocity of canoe (m2v2)

After the event:
Final momentum of the combined system = (mass of camper + mass of canoe) * (final velocity of the combined system)

Given:
mass of camper (m1) = 80 kg
velocity of camper (v1) = 4 m/s
combined mass (m1 + m2) = 110 kg

Using the conservation of momentum, we can set up the equation:

(mass of camper * velocity of camper) + (mass of canoe * velocity of canoe) = (mass of camper + mass of canoe) * (final velocity of the combined system)

Plugging in the given values:

(80 kg * 4 m/s) + (mass of canoe * velocity of canoe) = (110 kg) * (final velocity of the combined system)

At this point, we have an equation with two unknowns: mass of canoe and velocity of canoe. To solve for these unknowns, we'll need additional information, such as the velocity of the canoe (v2), which is not provided in the question.