Answer:
a) [tex]v = 2.886\,\frac{m}{s}[/tex], b) [tex]\mu_{k} = 0.014[/tex]
Explanation:
a) The final speed is determined by the Principle of Momentum Conservation:
[tex](62.2\,kg)\cdot (3.80\,\frac{m}{s} ) = (81.9\,kg)\cdot v[/tex]
[tex]v = 2.886\,\frac{m}{s}[/tex]
b) The deceleration experimented by the system person-sled is:
[tex]a = \frac{\left(0\,\frac{m}{s} \right)^{2}-\left(2.886\,\frac{m}{s} \right)^{2}}{2\cdot (30\,m)}[/tex]
[tex]a = -0.139\,\frac{m}{s^{2}}[/tex]
By using the Newton's Laws, the only force acting on the motion of the system is the friction between snow and sled. The kinetic coefficient of friction is:
[tex]-\mu_{k}\cdot m\cdot g = m\cdot a[/tex]
[tex]\mu_{k} = -\frac{a}{g}[/tex]
[tex]\mu_{k} = -\frac{\left(-0.139\,\frac{m}{s^{2}} \right)}{9.807\,\frac{m}{s^{2}} }[/tex]
[tex]\mu_{k} = 0.014[/tex]
