Calculating the Center of Mass of a Boat with 3 People

[Susanne217]

Homework Statement

Lets image the following a boat has three people in it

A has a mass of 120lb
B has a mass of 180lb
C has a mass of 160lb

and the boat has a mass of 120lb

also distance from person A to the front of the boat is 2 feet and distance from person A to person B is 8 feet and distance from person B to person C who is at the end of boat is 8 feet. What is the center of mass of the boat

Homework Equations

x = (m_1*x_1 + ...+ m_n * x_n)/M

where is the mass of all 3 people and the boat.

The Attempt at a Solution

the center of mass is then

$$x = \frac{120lb \cdot (2) + 180lb \cdot (8) + 160lb \cdot 16 }{120+180+160+120}$$

Is this right?

 

[Doc Al]

Make sure you measure the distance of each mass from the same point--for example, from the front of the boat. And don't forget the mass of the boat itself--where is it located?

 

[Susanne217]

Make sure you measure the distance of each mass from the same point--for example, from the front of the boat. And don't forget the mass of the boat itself--where is it located?

What I'm unsure about is the distance from each end of the boat is exactly 8 feet to the center of the boat is the mass of the boat by any chance the mass at the center of the boat + the mass of boat??

Which means is the mass at the center is 180lb and mass of the person is 120lb

then the mass of the boat is 300lb?

and I multiply this by 8 this to the top of center of mass fraction is previous post??

 

[Doc Al]

The mass of the boat is given as 120 lb. But the center of the boat is not 8 feet from the end. Hint: Use the distances given to figure out the length of the boat. (And the correct distance of each person from the end.) Draw yourself a diagram.

 

[Cilabitaon]

Consider this a rudimentary ascii of the boat and its passengers:
(F) is the front of the boat, ABC are the people and (B) is the back,with each hyphen(-)marking 1ft

(F)--A--------B--------C(B)
120 180 160

and we know that the boat is of mass 120lb, so that can be added where?

make sure you do what the Doc says and always calculate moments from the same point =].