Physics

Buoyancy.

A Team of 6 scouts plan to cross a lake on a raft they designed.
The dimensions of each plank is 30 cm x 30 cm x 3m.
The density of the wooden planks is of .80.
The average mass of the members is 65KG. And for their safety they want the top of the raft to be 3 cm above the surface of the water. How many wooden planks do they need to complete their project?

So far i found
V1 = .248
V = .27
P1 = .8
P = .73
using V1/V = P/P1.
Total mass of cargo ( scouts ) 6 x 65 = 390 KG. I really don't know where to go from here?!?!

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  1. Add the mass of scouts and N planks.
    That must equal the mass of displaced water.

    Plank mass (each) = 0.80*0.3*0.3*3*1000 kg/m^3
    = 216 kg

    Displaced water mass per plank:
    = 0.3*0.27*3*1000 kg/m^3
    = 243 kg

    390 + 216 N = 243 N

    N = 14.4 planks

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