91影视

The given data can be listed below,

• The mass of the open-faced boat is, $m_b=5750\mathrm{kg}$.
• The cargo thrown overboard is $20\%$.

A buoyant object will be buoyant due to the top and bottom forces. This is because height is directly proportional to the base and the top.

Buoyant force results from multiplying the difference between pressure and the area of the object, which corresponds to the net force on that object.

When a boat floats, so the buoyant force on it equals the weight of the object given by,

$B=m_{b}g$

Also, the buoyant force can be expressed as,

$B={蚁}_{w}gV$

Here, ${蚁}_w$is the density of water whose value is $\left(1.00脳{10}^3\mathrm{kg}/{\mathrm{m}}^3\right)$, V is the volume of the boat, and g is the acceleration due to gravity.

Equate the equations mentioned above; the volume of the boat can be calculated as,

$$\begin{gathered} {蚁}_{w}gV=m_{b}g \\ V=\frac{m_b}{{蚁}_w} \end{gathered}$$

Substitute values in the above equation.

$$\begin{gathered} V=\frac{5750\mathrm{kg}}{1.00脳{10}^3\mathrm{kg}/{\mathrm{m}}^3} \\ =5.75{\mathrm{m}}^3 \end{gathered}$$

Thus, the volume of the boat is $5.75{\mathrm{m}}^3$.

After cargo is thrown in water, 20% of the boat鈥檚 volume will be above water, so 80% of the boat is submerged.

The volume of the submerged boat is expressed as,

$V_{sub}=0.80V$

Here, V is the volume of the boat.

The mass of the submerged boat can be expressed as,

$m={蚁}_w{V}_{sub}$

Here, ${蚁}_w$is the density of water and $V_{sub}$is the volume of the boat submerged in water.

Substitute values in the above equation.

$$\begin{gathered} m={蚁}_w\left(0.80V\right) \\ =\left(1.00脳{10}^3\mathrm{kg}/{\mathrm{m}}^3\right)\left(0.80\right)\left(5.75{\mathrm{m}}^3\right) \\ =4600\mathrm{kg} \end{gathered}$$

The mass of cargo thrown out is calculated as,

$m_{cargo}=m_b-m_{sub}$

Substitute values in the above equation.

$$\begin{gathered} m_{cargo}=5750\mathrm{kg}-4600\mathrm{kg} \\ =1150\mathrm{kg} \end{gathered}$$

Thus, the mass of cargo thrown out by the captain must be $1150\mathrm{kg}$.