In a needle biopsy, a narrow strip of tissue is extracted from a patient using a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be fired into the patient's body by a spring. Assume that the needle has mass 5.60 g, the light spring has force constant 430 N/m, and the spring is originally compressed 8.35 cm to project the needle horizontally without friction. After the needle leaves the spring, the tip of the needle moves through 2.40 cm of skin and soft tissue, which exerts on it a resistive force of 7.60 N. Next, the needle cuts 3.50 cm into an organ, which exerts on it a backward force of 9.20 N.

(a) Find the maximum speed of the needle.

____________m/s

(b) Find the speed at which a flange on the back end of the needle runs into a stop that is set to limit the penetration to 5.90 cm.

______________m/s