Sam, whose mass is 72 kg , takes off across level snow on his jet-powered skis. The skis have a thrust of 190 N and a coefficient of kinetic friction on snow of 0.1. Unfortunately, the skis run out of fuel after only 9.0 s. How far has Sam traveled when he finally coasts to a stop?

Given Information:

Mass = 72 kg

Force exerted by ski = 190 N

coefficient of kinetic friction = 0.1

ski runs out of fuel after = 9 sec

Required Information:

Distance traveled when he stops = ?

d = 179.33 m

Explanation:

The problem can be divided into two parts

Part 1: before running out of fuel

In the first part, the forces acting on Sam are

Ski thrust and Force of friction

Force of friction = kmg

where k is the coefficient of kinetic friction, m is Sam's mass and g is gravity 9.8 m/s²

Force of friction = 0.1*72*9.8

Force of friction = 70.56 N

so the net force acting on Sam is

Fnet = ski thrust - force of friction

Fnet = 190 - 70.56

Fnet = 119.44 N

According to Newton's second law of motion

F = ma

a = F/m

a = 119.44/72

a = 1.65 m/s²

The distance traveled can be found using kinematic equation

d = vi + 0.5at²

d = 0 + 0.5*1.65*9²

d = 66.82 m

The speed at this point is

vf = (d + 0.5at²)/t

vf = (66.82 + 0.5(1.65)(9)²)/9

vf = 14.85 m/s

Part 2: after running out of fuel

When the fuel runs out the ski is no longer applying any force so the only force acting on Sam is force of friction

kmg = ma

kg = a

a = 0.1*-9.8

a = -0.98 (minus sign due to deceleration)

The distance traveled can be found using kinematic equation

2ad = vf² - vi²

d = (vf² - vi²)/2a

d = (vf² - vi²)/2a

d = (0² - 14.85²)/2*-0.98

d = 112.51 m

How far has Sam traveled when he finally coasts to a stop?

We have to sum the distance before and after Sam runs out of fuel because he stops after covering the sum of these distance

d = 66.82 + 112.51

d = 179.33 m

the arctic is a region of the planet, north of the arctic circle, and includes the arctic ocean, greenland, baffin island, other smaller northern islands, and the far northern parts of europe, russia (siberia), alaska and canada.

area of focus