Question

Kayaks have been used for thousands of years to hunt and fish in Arctic regions. The total volume of a particular kayak is 285 litres (which is 0.285 m3). It has a mass of 75 kg. The man using it has a volume of 0.066 m3. When sitting in the kayak, half of man’s volume is inside the kayak. The density of the human body is about 1000 kg/m3.Calculate the density of the empty kayak.

Answer 1

Given,

The volucme of Kayak, V₁=0.285 m³

The mass of the Kayak when the man is sitting in it, m₁=75 kg

The volume of the man, V₂=0.066 m³

The density of the man, d=1000 kg/m³

The mass of the man inside the Kayak is given by,

$m_2=V_2\times d$

On substituting the known values,

$\begin{gathered} m_2=0.066\times1000 \\ =66\text{ kg} \end{gathered}$

The mass of the empty Kayak is,

$\begin{gathered} M=m_1-m_2 \\ =75-66 \\ =9\text{ kg} \end{gathered}$

Given that only half of the volume of the man is inside the Kayak when he is sitting in it. Half of the man's volume which is outside the Kayak will be considered in the total volume of the Kayak when he is sitting in it. Thus we have to subtract half of his volume, which is outside the Kayak, while we calculate the density of the Kayak.

Thus the density of the empty Kayak is

$\rho=\frac{M}{V_1-\frac{V_2}{2}}$

On substituting the known values,

$\begin{gathered} \rho=\frac{9}{0.285-\frac{0.066}{2}} \\ =35.71kg/m^3 \end{gathered}$

Thus the density of the Kayak is 35.71 kg/m³