Question

A large 2.71 kg bird, searching for food, spots a large, 0.384 kg bug hovering in its vicinity. If the bird is traveling at 8.8 m/s, what will be his velocity immediately after nabbing the bug?

Answer 1

The initial momentum of the system can be given as,

$p_i=m_1u_1+m_2u_2$

The final momentum of the system can be expressed as,

$p_f=(m_1+m_2)v$

According to conservation of momentum,

$p_i=p_f$

Plug in the known expressions,

$\begin{gathered} m_1u_1+m_2u_2=(m_1+m_2)v \\ v=\frac{m_1u_1+m_2u_2}{m_1+m_2} \end{gathered}$

Substitute the known values,

$\begin{gathered} v=\frac{(2.71\text{ kg)(8.8 m/s)+(0.384 kg)(0 m/s)}}{2.71\text{ kg+0.384 kg}} \\ =\frac{23.848\text{ kgm/s}}{3.094\text{ kg}} \\ \approx7.71\text{ m/s} \end{gathered}$

Thus, the velocity after nabbing the bug is 7.71 m/s.