Answer :
Given data:
* The initial velocity of the object is 10m/s.
* The ratio of the final kinetic energy to the initial kinetic energy is half.
Soluiton:
The kinetic energy in terms of mass and velocity of the object is,
[tex]\begin{gathered} \frac{K_f}{K_i}=\frac{\frac{1}{2}mv^2}{\frac{1}{2}mu^2} \\ \frac{K_f}{K_i}=\frac{v^2}{u^2} \end{gathered}[/tex]where v is the final velocity and u is the initial velocity, K_f is the final kinetic energy, and K_i is the initial kinetic energy,
Substituting the known values,
[tex]\begin{gathered} \frac{1}{2}=\frac{v^2}{10^2} \\ v^2=\frac{100}{2} \\ v^2=50 \\ v=7.07\text{ m/s} \\ v\approx7.1\text{ m/s} \end{gathered}[/tex]Thus, the final velocity of the object is 7.1 m/s.
Hence, option C is the correct answer.