Question

Squids and octopuses propel themselves by expelling water. They do this by keeping water in a cavity and then suddenly contracting the cavity to force out the water through an opening. A 6.50-kg squid (including the water in the cavity) at rest suddenly sees a dangerous predator. (a) If the squid has 1.75 kg of water in its cavity, at what speed must it expel this water suddenly to achieve a speed of 2.50 m/s to escape the predator? Ignore any drag effects of the surrounding water. (b) How much kinetic energy does the squid create by this maneuver?

Answer 1

Answer:

6.78571 m/s

55.13387 Joules

Explanation:

$v_s$ = Velocity of squid = 2.5 m/s

$v_w$ = Velocity of water

$m_w$ = Mass of water = 1.75 kg

Mass of squid

$m_s=6.5-1.75=4.75\ kg$

Momentum of squid

$p_s=m_sv_s\\\Rightarrow p_s=4.75\times 2.5\\\Rightarrow p_s=11.875\ kgm/s$

As the momentum of the system is conserved

$p_s+p_w=0\\\Rightarrow p_s=-p_w\\\Rightarrow 11.875=-p_w\\\Rightarrow 11.875=-m_wv_w\\\Rightarrow v_w=-\frac{11.875}{1.75}\\\Rightarrow v_w=6.78571\ m/s$

The speed of the water is 6.78571 m/s

Kinetic energy the squid creates is given by

Kinetic energy of the squid + Kinetic energy of water

$K=K_s+K_w\\\Rightarrow K=\frac{1}{2}(m_sv_s^2+m_wv_w^2)\\\Rightarrow K=\frac{1}{2}(4.75\times 2.5^2+1.75\times 6.78571^2)\\\Rightarrow K=55.13387\ J$

Kinetic energy the squid creates by this maneuver is 55.13387 Joules