Question

A child in a boat throws a 5.80kg package out horizontally

with a speed of 10.0 m/s, Fig. 7-31.Calculate the velocity of the
boat immediately after, assuming itwas initially at rest. The mass
of the child is 29.0 kg and that of the boat is 50.0 kg. Ignore
water resistance. Find itsMagnitude.

Answer 1

0.734 m/s

Step-by-step explanation:

Since there's no external force outside the system, by the law of momentum conservation, momentum before the throw (which is 0) must be the same as after the throw:

`0 = m_pv_p + (m_c + m_b)v_b`

where m_p = 5.8 kg is the mass of the package

v_p = 10m/s is the velocity of the package

m_c = 29 kg is the mass of the child

m_b = 50 kg is the mass of the boat

As the package and the boat has opposite directions of motion, they should have opposite velocity:

`5.8*10 + (29 + 50)v_b = 0`

`b_b = (-58)/(79) = -0.734 m/s`

So the magnitude of the boat velocity is 0.734 m/s