Answer:
6.5 m
Explanation:
First of all, we need to compute the acceleration of the skier. We know that there is only force acting on the skier: the force of friction, which is in the opposite direction to the motion of the skier. Using 2nd Newton Law:
[tex]\sum F = ma\\F_f = ma\\-\mu m g = ma[/tex]
where [tex]F_f = -\mu mg[/tex] is the force of friction, with
[tex]\mu=0.220[/tex] is the coefficient of kinetic friction
m is the mass of the skier
[tex]g=9.8 m/s^2[/tex] is the acceleration due to gravity
Re-arranging the equation, we find:
[tex]a=\mu g=-(0.220)(9.8 m/s^2)=-2.16 m/s^2[/tex]
So now we can use the following SUVAT equation to calcualte the total displacement of the skier before stopping:
[tex]v^2 - u^2 = 2ad[/tex]
where
v = 0 is the final velocity
u = 5.30 m/s is the initial velocity
a = -2.16 m/s^2 is the acceleration
d = ? is the displacement
Solving the formula for d, we find:
[tex]d=\frac{v^2-u^2}{2a}=\frac{0-(5.30 m/s)^2}{2(-2.16 m/s^2)}=6.5 m[/tex]
