Physics problem?

Question

A boat has a weight of 1200 N and floats at a depth of 7 m. The area of the hull is 50 m^2.

1. What is the weight density of the sea water in which it is floating

2. At what depth will the boat float if a 600 N cargo is added ?
Show work

Answer 1

Since the boat floats, it displaces its mass, or in this case, weight. So teh weight of the water is 1200 N. Now the boat occuppies a volume in the water, V given by

V= depth of hull below water x area of hull in water
= 7 m x 50 m^2 = 350 m^3

Then weight density = weight of water/volume = 1200N/350 m^3 = 324.9 Nt/m^3

If you add 600 Nt to the boat and it still floats, it has to displace 1800 Nt of water. We know the weight density from part 1, call that W. Since

W = weight/volume = (Weigth of boat +cargo)/(area of hull x depth)

then

depth = (weigth of boat + cargo)/(W*area of hull)
= 1800N/(342.9 Nt/m^3*50 m^2)
= 10.5 m