Respuesta :
Answer:
r = 3858.7635 m
Explanation:
first we will use the law of newton as:
-mg+N = 0
N = mg
where m is the mass, g the gravity and N is the normal force, So:
N = (75)(9.8)
N = 735
also, when the skis had fuel:
F-[tex]F_k[/tex] = ma
where F is the force of the skis, [tex]F_k[/tex] is the force by the kinetic friction and a is the aceleration.
so:
F-[tex]U_kN[/tex] = ma
200N-(0.1)(735) = (75)a
[tex]U_k[/tex] is the coefficient of kinetic friction on water, therefore solving for a:
a = 1.687 m/s^2
so, with the aceleration we can find the velocity V of jason just after the skis run out of fuel as:
V = at
V = (1.687m/s^2)(41s)
V = 69.167 m/s^2
Where t is the time in which the skis run out of fuel. Now using the law of the conservation of energy we will find the distance as:
Initial Energy - Final Energy = Work of Friction
[tex]\frac{1}{2}MV^2 = U_kNd[/tex]
[tex]\frac{1}{2}(75)(69.167)^2 = (0.1)(735)d[/tex]
d = 2440.8m
that means that jason traveled 2440.8m after the skis run out of fuel.
Additionally, the distance x that jason traveled with fuel is calculated as:
x = [tex]\frac{1}{2}at^2[/tex]
x = [tex]\frac{1}{2}(1.687)(41)^2[/tex]
x = 1417.9235 m
Finally, Jason travel 3858.76 m when he finally coast to a stop. It is calculated as:
r = x + d
r = 1417.9235+2440.8
r = 3858.7635 m
