Question

Squids rely on jet propulsion to move around. A 1.50 kg squid (including the mass of water inside the squid) drifting at 0.40 m/ssuddenly ejects 0.14 kg of water to quickly get itself moving at 2.50 m/s.If drag is ignored over the small interval of time needed to expel the water (the impulse approximation), what is the water's ejection speed relative to the squid?

Answer 1

Answer:

-22.5 m/s

Explanation:

$m_1$ = Mass of squid = 1.5 kg

$m_2$ = Mass of water ejected = 0.14 kg

$v_1$ = Velocity of squid = 0.4 m/s

$v_2$ = Velocity of squid after ejection = 2.5 m/s

v = Velocity of water ejection

In this system the momentum is conserved

$m_1v_1+(m_1-m_2)v_2+m_1v=0\\\Rightarrow 1.5\times 0.4-2.5(1.5-0.14)-1.5v=0\\\Rightarrow v=\frac{-1.5\times 0.4+(1.5-0.14)\times 2.5}{-0.14}\\\Rightarrow v=-20\ m/s$

The velocity of the water ejection relative to the squid is

-20+(-2.5) = -22.5 m/s

The negative sign indicates the opposite direction to the direction of the squid.