Squids and octopuses propel themselves by expelling water. They do this by takin

Question

Squids and octopuses propel themselves by expelling water. They do this by taking the water into a cavity and then suddenly contracting the cavity, forcing the water to shoot out of an opening. A 6.20kg squid (including the water in its cavity) that is at rest suddenly sees a dangerous predator.

A. If this squid has 1.50kg of water in its cavity, at what speed must it expel the water to suddenly achieve a speed of 2.30m/s to escape the predator? Neglect any drag effects of the surrounding water.

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

Please show ansewer as well as equation

Explanation / Answer

Mass of the squid (including water in it's cavity) is, mt = 6.2 kg

Initial velocity of this squid is, vit = 0 m/s

A.

Mass of water in the cavity of the squid is, mw = 1.5 kg.

Thus, mass of the squid minus the water is, ms = (6.2 - 1.5) kg = 4.7 kg

Final speed of the squid is, vfs = 2.3 m/s

Using the law of conservation of momentum, we can write,

mt vit = ms vfs + mw vfw

where vfw is the speed with which the water is expelled from the cavity of the squid.

6.2 * 0 = 4.7 * 2.3 + 1.5 * vfw

vfw = -7.206666667 m/s = -7.21 m/s

Negative sign indicates that this velocity is in opposite direction of the velocity of the squid.

B.

Kinetic energy created by the squid for this escape maneuver is,

T = (1/2 msvfs2) + (1/2 mwvfw2)

T = 0.5 * 4.7 * 2.3 * 2.3 + 0.5 * 1.5 * (-7.21) (-7.21)

T = 51.419575 J = 51.42 J

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