A 113 kg man sits on the stern of a 6.3 m long boat. The prow of the
boat touches the pier, but the boat isn’t tied. The man notices his
mistake, stands up and walks to the boat’s prow, but by the time he
reaches the prow, it’s moved 3.26 m away from the pier. Assuming no
water resistance to the boat’s motion, calculate the boat’s mass (not
counting the man).

m = 105.37 kg

Explanation:

We are given;

Mass of man; m = 113 kg

Length of boat = 6.3m

Now, The position of the center of mass will not change during the motion of the man.

Thus,

X_g,i = X_g,f

So,

[113(6.3) + ma]/(113 + m) = [113(3.26) + m(a +3.26)]/(113 + m)

113 + m will cancel on both sides to give;

113(6.3) + ma = [113(3.26) + m(a +3.26)]

711.9 + ma = 368.38 + ma + 3.26m

ma will cancel out to give;

711.9 - 368.38 = 3.26m

343.52/3.26 = m

m = 105.37 kg