Needle Biopsy - Physics - 10 points first correct procedure!?

Question

In a needle biopsy, a narrow strip or cylinder of tissue is
extracted from a patient with a hollow needle. Rather than
pushed by hand, to ensure a clean cut the needle can be “fired”
into the tissue with a spring or a burst of air. Suppose that the
tip of the needle moves through 2.40 cm of skin and soft tissue,
which exerts a a resistive force of 7.60 N. If the mass of the
needle is 5.6 g, what must be the velocity of the needle as it
first enters the patients body?

The procedure is most important!

Answer 1

The amount of work require to penetrate the skin is

W=F d
W - work
F - force
d - distance

To do so the needle must have a kinetic energy (Ke) equal to that work (W).

Ke=.5 mv^2

so
since .5mv^2=Fd
v=sqrt(2 F d /m)
v=sqrt(2 x 7.60 x 0.024/5.6E-3)
v=8.07 m/s