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 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?

Answer 1

a. 9.9806 m/s

b. 97.31J

Step-by-step explanation:

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

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

`P=\sum P_i`,
`P=mv`

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

#We neglect any external forces such as drag effects:

#mass of the squid:

`m_s=M-M_w\\\\=7.50-1.55\\\\=5.95kg`

#For momentum,

`P=mv\\\\=5.95*2.6\\\\=15.47\ kg.m/s`

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

`P_s+P_w=0\\\\15.47\ kg.m/s+P_w=0\\\\P_w=-15.47\ kg.m/s`

From the equation
`P=mv:\\`

`-15.47\ kg.m/s=1.55v_w\\\\v_w=-9.9806\ m/s`

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:

`K_s=(1)/(2)m_sv_s\\\\=0.5*5.95* 2.6^2\\\\=20.11J`

The kinetic energy of the water is :

`K_w=(1)/(2)m_wv_w\\\\=0.5*1.55* 9.9806^2\\\\=77.20J`

Total kinetic energy:

`K_t=K_s+K_w\\\\=20.11J+77.20J\\\\=97.31J`

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