A stationary boat of mass 160 kg floats on water. The mast of the boat is vertical. A sack of mass 23 kg is thrown at the boat, as shown in Figure 2.1.

Figure 2.1, a stationary boat of mass 160 kg floating on water with a vertical mast; a sack is shown approaching the mast horizontally at 3.4 m s$^{-1}$, with an arrow pointing from the sack towards the mast

Immediately before colliding with the mast of the boat, the sack is travelling horizontally with a speed of 3.4 m s

^{- 1}

. The sack collides with the mast and remains in contact with it, without rebounding. Assume that resistive forces acting on the boat during the collision are negligible.

2(b)(i)Momentum Impulse CollisionsMedium2 marks

Calculate the horizontal speed

v

of the sack and boat immediately after the collision.

2(b)(ii)Momentum Impulse CollisionsMedium3 marks

The total kinetic energy of the sack and boat immediately before the collision is

E_{1}

. The total kinetic energy of the sack and boat immediately after the collision is

E_{2}

. Determine the ratio

\frac{E _{2}}{E _{1}}

2(b)(iii)Momentum Impulse CollisionsMedium1 mark

State and explain whether the collision between the sack and boat is elastic or inelastic.

Answer

0 words

2(c)

After a short time, the boat in 2(b) is at rest again.

2(c)(i)Upthrust BuoyancyEasy1 mark

Show that the upthrust acting on the boat with the sack is 1800 N.

Answer

0 words

2(c)(ii)Upthrust BuoyancyMedium2 marks

The boat displaces water with a volume of

1.80 \times 1 0^{5}

^{3}

. Calculate the density of the water. Give your answer to 3 significant figures.

Answer