A 44.0-kg woman stands at one end of a 148 kg raft that is 6 m long. The other end of the raft is 0.5 m from a pier.
(a) The woman walks toward the pier until she gets to the other end of the raft and stops there. Now what is the distance between the raft and the pier? in m please
(b) How far did the woman walk (relative to the pier)? in m please
I tried the following:
(44*5)+(148*0.5)/(44+148) but i get the wrong answer I don't know what I am doing wrong! And for b I don't know how to do that! Please help am confused! Thank you.
They want you to neglect friction between the boat and the water. With that assumption, the center of mass of the boat and woman remain in the same place, relative to the pier. When she stops walking, the boat stops moving.
Let X be the distance of the close end of the boat from the pier. Initially
X = Xi = 0.5 m. Afterwards, X = Xf. You want to know the value of Xf.
Initial CM location =
[148*3.5 + 44*6.5]/(148+44) = 4.188 m
Final CM location =
[148*(3+Xf) + 44*Xf]/192 = 4.188
Solve for Xf
804= 444 + 148 Xf + 44 Xf
360 = 192 Xf
Xf = 1.875 m
The boat ends up farther from the pier, although the woman ends up closer to it.
(b) The woman was initially 6.5 m from the pier and ended up 1.875 m away. She moved 4.625 m closer, relative to the pier.
Thank you Drwls! I really appreciate your help.
To solve part (a), you need to consider the principle of conservation of linear momentum. The initial momentum of the system, consisting of the woman and the raft, is zero, and it remains zero after she walks.
To find the distance between the raft and the pier, you can start by setting up an equation based on the conservation of momentum:
(44 kg) * (distance walked by the woman) = (148 kg) * (distance between the raft and the pier)
Let's represent the distance walked by the woman as x and the distance between the raft and the pier as y. We can rewrite the equation as:
(44 kg) * x = (148 kg) * y
Now, we can rearrange the equation to solve for y:
y = (44 kg * x) / (148 kg)
Plugging in the values, we have:
y = (44 kg * 6 m) / (148 kg) = 1.32 m
Therefore, the distance between the raft and the pier is 1.32 meters.
Now, let's move on to part (b). To find how far the woman walked relative to the pier, you need to calculate the total distance she walked, including the initial distance between her starting point and the pier.
Since the initial distance from the woman to the pier is 0.5 m, and she walks for 6 m, the total distance she walks relative to the pier would be:
Total distance = Initial distance + Distance walked
= 0.5 m + 6 m
= 6.5 m
Therefore, the woman walked 6.5 meters relative to the pier in part (b).