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 7.50 kg squid (including the water in the cavity) at rest suddenly sees a dangerous predator.

A. If the squid has 1.55 kg of water in its cavity, at what speed must it expel this water to suddenly achieve a speed of 2.60 m/s to escape the predator? Neglect any drag effects of the surrounding water.

B. How much kinetic energy does the squid create by this maneuver?

Mass of squid with water in cavity is M=7.5kg, the water has a mass of [tex]M_w=1.55kg[/tex] and the squid's velocity after releasing the water is [tex]v_s=2.6m/s[/tex]

a. The total momentum of a system is the vector sum of its individual particles momenta;

[tex]P=\sum P_i[/tex], [tex]P=mv[/tex]

#For an isolated system, the momentum is conserved, p=k

#We neglect any external forces such as drag effects:

#mass of the squid:

[tex]m_s=M-M_w\\\\=7.50-1.55\\\\=5.95kg[/tex]

#For momentum,

[tex]P=mv\\\\=5.95\times2.6\\\\=15.47\ kg.m/s[/tex]

#The momentum for the squid initially at rest is zero;

[tex]P_s+P_w=0\\\\15.47\ kg.m/s+P_w=0\\\\P_w=-15.47\ kg.m/s[/tex]

From the equation [tex]P=mv:\\[/tex]

[tex]-15.47\ kg.m/s=1.55v_w\\\\v_w=-9.9806\ m/s[/tex]

Hence, water is expelled at a speed of 9.9806m/s( in opposite direction).

b. We use the mass and velocity of the squid to calculate it's kinetic energy:

[tex]K_s=\frac{1}{2}m_sv_s\\\\=0.5\times5.95\times 2.6^2\\\\=20.11J[/tex]

The kinetic energy of the water is :

[tex]K_w=\frac{1}{2}m_wv_w\\\\=0.5\times1.55\times 9.9806^2\\\\=77.20J[/tex]

Total kinetic energy:

[tex]K_t=K_s+K_w\\\\=20.11J+77.20J\\\\=97.31J[/tex]

Hence, the kinetic energy created by the squid is 97.31J