Answer:
Step-by-step explanation:
A. To find Sam's top speed, we need to calculate the net force acting on him and use it to calculate his acceleration. Since he is moving at a constant speed, we know that his acceleration is zero. Therefore, the net force on him must be zero. The forces acting on Sam are the force of thrust from the skis and the force of friction between the skis and the snow.
The force of thrust is 220 N. The force of friction is given by:
friction = coefficient of friction × normal force
The normal force is equal to Sam's weight, which is given by:
weight = mass × gravity = 78 kg × 9.8 m/s^2 = 764.4 N
Therefore, the force of friction is:
friction = 0.1 × 764.4 N = 76.44 N
The net force is:
net force = thrust - friction = 220 N - 76.44 N = 143.56 N
Using Newton's second law, we can find Sam's acceleration:
net force = mass × acceleration
143.56 N = 78 kg × acceleration
acceleration = 1.838 m/s^2
Sam's top speed can be found using the kinematic equation:
v^2 = v0^2 + 2aΔx
where v0 is Sam's initial speed (which is zero), a is his acceleration, and Δx is the distance he travels before he runs out of fuel. Rearranging this equation, we get:
v = sqrt(2aΔx)
Plugging in the values, we get:
v = sqrt(2 × 1.838 m/s^2 × 14 s) = 7.96 m/s
Therefore, Sam's top speed is 7.96 m/s.
B. To find how far Sam travels before he runs out of fuel, we can use the kinematic equation:
Δx = v0t + (1/2)at^2
where v0 is Sam's initial speed (which is zero), a is his acceleration, and t is the time it takes for him to run out of fuel (which is 14 s). Plugging in the values, we get:
Δx = (1/2)at^2 = (1/2) × 1.838 m/s^2 × (14 s)^2 = 227.1 m
Therefore, Sam travels 227.1 meters before he coasts to a stop.