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 Homework Statement
 Dr. Jane is ready to inject medicine into Bob. The hypodermic syringe she uses contains a medicine with the same density as water. The barrel of the syringe has a crosssectional area of 2.50 x 10^5 m^2. The crosssectional area of the needle is 1.0 x 10^8 m^2. In the absence of a force on the plunger, the pressure everywhere is atmospheric pressure. A 2.0 N force is exerted on the plunger, making medicine squirt from the needle to insure there is no air in the needle prior to giving the shot. Determine the speed of the emerging fluid. Assume that the pressure in the needle remains at atmospheric pressure, that the syringe is horizontal, and the speed of the emerging fluid is the same as the speed of the fluid in the needle.
 Homework Equations

(P1) + ρg(y1) + 0.5ρ(v1)^2 = (P2) + ρg(y2) + 0.5ρ(v2)^2
P=F/A
(A1)(v1) = (A2)(v2)
Did I do this problem correctly? I felt like I did this wrong because the answer is suppose to be around 50 m/s.