To solve the problem it is necessary to apply conservation of the moment and conservation of energy.
By conservation of the moment we know that
[tex]MV=mv[/tex]
Where
M=Heavier mass
V = Velocity of heavier mass
m = lighter mass
v = velocity of lighter mass
That equation in function of the velocity of heavier mass is
[tex]V = \frac{mv}{M}[/tex]
Also we have that [tex]m/M = 1/7 times[/tex]
On the other hand we have from law of conservation of energy that
[tex]W_f = KE[/tex]
Where,
W_f = Work made by friction
KE = Kinetic Force
Applying this equation in heavier object.
[tex]F_f*S = \frac{1}{2}MV^2[/tex]
[tex]\mu M*g*S = \frac{1}{2}MV^2[/tex]
[tex]\mu g*S = \frac{1}{2}( \frac{mv}{M})^2[/tex]
[tex]\mu = \frac{1}{2} (\frac{1}{7}v)^2[/tex]
[tex]\mu = \frac{1}{98}v^2[/tex]
[tex]\mu = \frac{1}{g(98)(5.1)}v^2[/tex]
Here we can apply the law of conservation of energy for light mass, then
[tex]\mu mgs = \frac{1}{2} mv^2[/tex]
Replacing the value of [tex]\mu[/tex]
[tex]\frac{1}{g(98)(5.1)}v^2 Â mgs = \frac{1}{2}mv^2[/tex]
Deleting constants,
[tex]s= \frac{(98*5.1)}{2}[/tex]
[tex]s = 249.9m[/tex]
