Question

(20 points) You are at the center of a boat and have been rowing the boat for a long time. You weigh only 80 kg and your 120 kg buddy Bubba has been riding at the front of your 60 kg, 4 m long boat. You come to a stop in the water and then switch places. A) What is the center of mass before you switch places

Answer 1

Step-by-step explanation:

From the given information:

Let the first weight be
`m_ 1` = 80 kg

The weight of the buddy be
`m_2` = 120 kg

The weight of Bubba be
`m_3` = 60 kg

Also, since you and Budda are a distance of 4m to each other, then the length to which both meet buddy will be:

`x_1 = x_3 = (4)/(2) \\ \\ = 2`

The length of the boat be
`x_2` = 4 m

∴

We can find the center of mass of the system by using the formula:

`X_(CM) = (m_1x_1+m_2x_2+m_3x_3)/(m_1+m_2+m_3) \\ \\ X_(CM) = ((80 * 2)+(120*4)+(60*2))/(80+120+60) \\ \\ X_(CM) = (160+480+120)/(260) \\ \\ \mathbf{X_(CM) = 2.923}`