Answer:0.46
Explanation:
Given
Initial height [tex]h=50 m[/tex]
inclination [tex]\theta =10^{\circ}[/tex]
Thrust[tex]=280 N[/tex]
combined mass of kieran and skis [tex]m=50 kg[/tex]
Speed at the bottom [tex]v=40 m/s[/tex]
From Work Energy Theorem
Work done by all the force is equal to change in kinetic Energy
[tex]W_{gravity}+W_{friction}+W_{thrust}=\frac{1}{2}mv^2-0[/tex]------------1
distance traveled along the slope [tex]x=\frac{50}{\sin 10}=287.93 m[/tex]
[tex]W_{gravity}=mgh=50\times 9.8\times 50=24500 J[/tex]
[tex]W_{thrust}=F\times x=280\times 287.93=80,620.4 J[/tex]
[tex]W_{friction}=-\mu mg\cos 10[/tex]
substitute in 1
[tex]24,500+80,620.4+W_{friction}=\frac{1}{2}\times 50\times 1600[/tex]
[tex]W_{friction}=40,000-24,500-80,620.4[/tex]
[tex]-\mu \cdot 50\times 9.8\times 287.93=-65,120.4[/tex]
[tex]\mu =\frac{65,120.4}{141,085.7}=0.46[/tex]
