Question

Several teenagers swim toward a rectangular, wooden raft that is 2.00 m wide and 2.50 m long. If the raft is 9.80 cm thick, how many 75.0 kg teenage boys can stand on top of the raft without the raft becoming submerged? Assume the wood density is 650 kg/m3.

Answer 1

2

Step-by-step explanation:

length of the raft, L = 2 m

Width of the raft, W = 2.5 m

height of the raft, H = 9.8 cm = 0.098 m

mass of each person, m = 75 kg

Density of wood = 650 kg/m^3

volume of raft, V = L x W x H = 2 x 2.5 x 0.098 = 0.49 m^3

let there are N persons

According to the principle of floatation

Buoyant force acting on the raft = True weight of the raft

Volume x density of water x g = volume x density of wood x g + N x mg

0.49 x 1000 x g = 0.49 x 650 x g + N x 75 x g

490 = 318.5 + N x 75

N = 2.28

So, the maximum number of person is 2.