A 770N woman sitting on a frictionless surface throw a 2.6 kg book at a speed of 35 m/s. What is her recoil speed in m/s?

Use conservation of momentum. Total momentum (m v) will remain zero. Her momentum and the stone's momentum will be equal, but in opposite directions.

The woman's mass is 770/9.81 = 78.5 kg

78.5*V = 2.6*35

Solve for V