Answer:
The recoil velocity is 0.2687 m/s.
Explanation:
∵ The person is sitting on an icy surface , we can assume that the surface is frictionless.
∴ There is no force acting acting on the person and book as a system in horizontal direction.
Hence , momentum is conserved for this system in horizontal direction of motion.
If 'i' and 'f' be the initial and final states of this system , then by principle of conservation of momentum(p) -
=
System initially is at rest
∴=0
∴ From the above 2 equations
=0
We know that ,
Momentum(p)=Mass of the body(m)×velocity of the body(v)
Let and
be the mass of the person and the book respectively and
and
be the final velocities of the person and book respectively.
∴=
+
=0
From the question ,
= 74.9 kg
= 2.44 kg
= 8.25 m/s
Substituting these values in the above equation we get ,
(74.9 × )+ (2.44×8.25) = 0
∴ = - 0.2687 m/s (Negative sign suggests that the motion of the person is opposite to that of the book)
∴ The recoil velocity is 0.2687 m/s.