Canoe Movement Calculations: 45kg Woman in a 60kg Canoe

[marialo]

i'm having a problem with this one:
45kg woman is in a 60kg canoe of length 5m. They are initially at rest. she walks from a point 1m from the end to a point 1m from the other end where she stops. If resistance and the motion of the canoe in the water are ignored, how far does the canoe move during the process.

I thought this was a center of mass problem, but the center of mass doesn't change because the woman begins at rest. i don't know where to start...

 

[Astronuc]

How about conservation of momentum?

Hint: the magnitude of velocity (speed) = distance/time, and the time is the same.

Action-reaction.

 

[quicknote]

I would approach this problem by first identifying the relevant variables and equations that can be used to solve it. In this case, the variables are the mass of the woman (45kg), the mass of the canoe (60kg), the length of the canoe (5m), and the distance the woman moves (1m). The equation that relates these variables is the conservation of momentum equation, which states that the total momentum of a system remains constant unless acted upon by an external force.

Since the woman and canoe are initially at rest, the total momentum of the system is zero. When the woman moves from one end of the canoe to the other, she transfers her momentum to the canoe. This causes the canoe to move in the opposite direction with the same momentum. Therefore, the distance the canoe moves can be calculated by using the momentum equation:

p = mv

Where p is the momentum, m is the mass, and v is the velocity. Since the initial momentum of the system is zero, we can set the final momentum equal to zero as well:

0 = (45kg)(v1) + (60kg)(v2)

Where v1 is the velocity of the woman and v2 is the velocity of the canoe. Since the woman and canoe move in opposite directions, we can set v1 = -v2. Solving for v2, we get:

v2 = -3/4v1

Next, we can use the distance equation to relate the velocity and distance:

d = vt

Where d is the distance, v is the velocity, and t is the time. Since the woman and canoe move together, they have the same time interval. Therefore, we can set the distance of the woman (1m) equal to the distance of the canoe (d):

1m = v1t = v2t

Substituting v2 = -3/4v1, we get:

1m = -3/4v1t

Solving for t, we get:

t = 4/3s

Finally, we can use the distance equation again to calculate the distance the canoe moves:

d = v2t = (-3/4v1)(4/3s) = -1m

Therefore, the canoe moves a distance of 1m in the opposite direction. This calculation assumes that there is no resistance and the motion of the canoe in the water is ignored. In reality,