Question

8.92 A 45.0 kg woman stands up in a 60.0 kg canoe 5.00 m long. She walks from a point 1.00 m from one end to a point I .00 m from the other end (Fig. P8.92). If you ignore resistance to motion Of the canoe in the water, how far does the canoe move during fis process

Answer 1

The distance that the canoe moves in this process is 1.29 meters.

We first have to find the center of mass

$X = \frac{MsXs+McXc}{Mw+Mc}$

Where

Ms = Woman's mass = 45

Mc = Canoe's mass = 60kg

Xs = position from left= 1 cm

Xc = position from left end of canoe's mass = 2.5cm

When we put these values into the equation we have:

$X=\frac{45*1+60*2.5}{45+60} \\\\= 1.857$

The center of gravity lies at the center of this boat. Therefore,

$Xc = \frac{L}{2} \\\\L = 5 m long\\\\\frac{5}{2} =2.5$

5.00 - 1. 00 = 4 meters

$\frac{45*4+60*2.5}{45+60} = 3.14meters$

To get the distance that is moved by this canoe

distance = 3.143-1.857

= 1.286

≈ 1.29 meters

The distance that the canoe moves in this process is 1.29 meters.

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