Chapter 7, Problem 4P

To determine

The velocity of the boat, after throwing the package from the boat.

Answer to Problem 4P

Velocity of the boat will be 0.901 m/s in the opposite direction of the motion of the package.

Explanation of Solution

Given:

Velocity of the package is v = 10 m/s.

Mass of the boat is M = 45 kg

Mass of the child is m = 26 kg

Mass of the package is m₁= 6.4 kg.

Formula used:

According to conservation of momentum, initial momentum is same as final momentum.

  $m_i{v}_i=m_f{v}_f$

Calculation:

Initial velocity of both the objects is 0.

According to conservation law, momentum of the package will be same as the momentum of child and boat, but will be in opposite direction.

Let the velocity of the boat and child be V, then from the conservation of momentum,

  $\left(M+m+m_1\right)v_i=\left(m+M\right)V+m_{1}v$

Substituting the values,

  $\begin{array}{c}0=\left(26+45\right)V+\left(6.4\times 10\right)\\ V=-\frac{64}{\left(26+45\right)}\\ =-0.901\text{m}/\text{s}\end{array}$

Conclusion:

Therefore, the required velocity is 0.901 m/s in opposite direction of package.