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 1.55 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) The speed of the water must be 8.30 m/s.

B) Total kinetic energy created by this maneuver is 70.12 Joules.

Step-by-step explanation:

A) Mass of squid with water = 6.50 kg

Mass of water in squid cavuty = 1.55 kg

Mass of squid =
`m_1=6.50 kg- 1.55 kg=4.95 kg`

Velocity achieved by squid =
`v_1=2.60 m/s`

Momentum gained by squid =
`P=m_1v_1`

Mass of water =
`m_2=1.55 kg`

Velocity by which water was released by squid =
`v_2`

Momentum gained by water but in opposite direction =
`P'=m_2v_2`

P = P'

`m_1v_1=m_2v_2`

`v_2=(m_1v_1)/(m_2)=(4.95 kg* 2.60 m/s)/(1.55 kg)=8.30 m/s`

B) Kinetic energy does the squid create by this maneuver:

Kinetic energy of squid = K.E =
`(1)/(2)m_1v_1^(2)`

Kinetic energy of water = K.E' =
`(1)/(2)m_2v_2^(2)`

Total kinetic energy created by this maneuver:

`K.E+K.E'=(1)/(2)m_1v_1^(2)+(1)/(2)m_2v_2^(2)`

`=(1)/(2)* 4.95 kg* (2.60 m/s)^2+(1)/(2)* 1.55 kg* (8.30 m/s)^2=70.12 Joules`