When it is threatened, a squid can escape by expelling a jet of water, sometimes

Question

When it is threatened, a squid can escape by expelling a jet of water, sometimes colored with camouflaging ink. Consider a squid originally at rest in ocean water of constant density 1030 kg/m^3. Its original mass is 91.5 kg, of which a significant fraction is water inside its mantle. It expels this water through its siphon, a circular opening of diameter 3.00 cm, at a speed of 19.0 m/s. (a) As the squid is just starting to move, the surrounding water exerts no drag force on it. Find the squid's initial acceleration. (b) To estimate the maximum speed of the escaping squid, model the drag force of the surrounding water as described by R = 1/2 D rho Av^2 . Assume that the squid has a drag coefficient of 0.300 and a cross-sectional area of 890 cm^2. Find the speed at which the drag force counterbalances the thrust of its jet. please show me all the steps.

Explanation / Answer

we can use formula for thrust force on a rocket in this case
thrust force,F = uE
u = relative velocity between ejected material and rocket
E = rate of mass of ejection
in question
u = 19 m/s
E = density of water*((0.03/2)^2)*u

assuming water inside squid is pure water with density 1000 kg/m^3

E = 13.43 kg/s

thrust force,F = uR=255.176 N

a)acceleration,a = F/m = 255.176/91.5 = 2.789 m/s^2

b)drag force,R = 0.5*0.3*1030*(890*10^-4)*v^2 = 13.7505v^2

equatin

F = R gives v = 4.31 m/s Ans

if answer is wrong please try using the density of water inside squid body as same as density of ocean water to calculate E and follow same procedure

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