Respuesta :
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) -
[tex]p_{i}[/tex]=[tex]p_{f}[/tex]
System initially is at rest
∴[tex]p_{i}[/tex]=0
∴ From the above 2 equations
[tex]p_{f}[/tex]=0
We know that ,
Momentum(p)=Mass of the body(m)×velocity of the body(v)
Let [tex]m_{1}[/tex] and [tex]m_{2}[/tex] be the mass of the person and the book respectively and [tex]v_{1}[/tex] and [tex]v_{2}[/tex] be the final velocities of the person and book respectively.
∴[tex]p_{f}[/tex]=[tex]m_{1}[/tex][tex]v_{1}[/tex]+[tex]m_{2}[/tex][tex]v_{2}[/tex]=0
From the question ,
[tex]m_{1}[/tex] = 74.9 kg
[tex]m_{2}[/tex] = 2.44 kg
[tex]v_{2}[/tex] = 8.25 m/s
Substituting these values in the above equation we get ,
(74.9 × [tex]v_{1}[/tex] )+ (2.44×8.25) = 0
∴[tex]v_{1}[/tex] = - 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.
