Answer:
17.10 m
Explanation:
When the toboggan stops, we have:
[tex]N-w_y=0\\F-w_x=0[/tex]
The x-component of weight is the product of the weight and the sine of the angle above the horizontal, so the y-component of W is the product of the weight and the cosine of the angle above the horizontal.
[tex]N-mgcos(25^\circ)=0\\F-mgsin(25^\circ)=0\\F=mgsin(25^\circ)(1)[/tex]
The work-energy principle states that the change in the kinetic energy of an object is equal to the net work done on the object.
[tex]\Delta K=W\\K_f-K_i=F\cdot h\\\frac{m(v_f)^2}{2}-\frac{m(v_i)^2}{2}=Fhcos(180^\circ)[/tex]
Recall that [tex]v_f=0[/tex], replacing (1):
[tex]-\frac{m(v_i)^2}{2}=mgsin(25^\circ)h(-1)\\h=\frac{(v_i)^2}{2gsin(25^\circ)}\\h=\frac{(11.9\frac{m}{s})^2}{2(9,8\frac{m}{s^2})sin(25^\circ)}\\h=17.10 m[/tex]
