A 60.0-kg skier with an initial speed of 12.0 m/s coasts up a 2.50-mhigh rise and angle is 35 degrees.Find her final speed at the top, given that the coefficient of friction between her skis and the snow is 0.0800. (Hint: Find the distance traveled up the incline assuming a straight-line path as shown in the figure.)

Why did the skier go up the hill? Because it was inclined to be fun! Okay, let's tackle this problem.

First, let's find the distance traveled up the incline. We can use the formula for the distance covered along an inclined plane:

distance = height / sin(angle)

Plugging in the values, we get:

distance = 2.50 m / sin(35 degrees)

Now, let's find the work done by friction during the skier's ascent. The work done by friction is equal to the force of friction multiplied by the distance traveled. The force of friction is given by:

force of friction = coefficient of friction * weight

The weight can be calculated using:

weight = mass * gravitational acceleration

So:

force of friction = coefficient of friction * (mass * gravitational acceleration)

Now, let's find the work done by the force of gravity during the skier's ascent. The work done by gravity is equal to the weight multiplied by the vertical distance traveled. The vertical distance traveled is equal to the height of the rise:

work done by gravity = weight * height

Now, let's find the net work done during the skier's ascent. The net work done is equal to the work done by friction plus the work done by gravity:

net work done = work done by friction + work done by gravity

Finally, let's find the final velocity at the top. The final velocity can be found using the equation:

final velocity = initial velocity + (net work done / mass)

Now, let's calculate it all and create a circus of physics:

First, we need to find the distance traveled up the incline:

distance = 2.50 m / sin(35 degrees)

Next, we can calculate the force of friction:

force of friction = 0.080 * (60.0 kg * 9.8 m/s^2)

Now, let's find the work done by gravity:

work done by gravity = (60.0 kg * 9.8 m/s^2) * 2.50 m

Now, let's find the net work done:

net work done = work done by friction + work done by gravity

Finally, let's find the final velocity at the top:

final velocity = 12.0 m/s + (net work done / 60.0 kg)

Whew! That was a lot of calculations. I hope you enjoyed this physics circus act!

To find the final speed of the skier at the top, we need to follow these steps:

Step 1: Determine the work done against friction during the climb.
Step 2: Calculate the work done against gravity during the climb.
Step 3: Use the work-energy principle to find the change in kinetic energy.
Step 4: Calculate the final speed.

Let's start with Step 1:

Step 1: Determine the work done against friction during the climb.

The work done against friction can be calculated using the formula:

Work_friction = force_friction * distance

The force of friction can be calculated using the equation:

force_friction = coefficient_friction * normal_force

where the normal force is equal to the weight of the skier, which can be calculated using the formula:

normal_force = mass * gravity

The distance traveled up the incline can be calculated using trigonometry:

distance = height / sin(angle)

Using the given values:

mass = 60.0 kg
coefficient_friction = 0.0800
height = 2.50 m
angle = 35 degrees
gravity = 9.8 m/s^2

Substituting these values into the equations:

normal_force = mass * gravity
normal_force = 60.0 kg * 9.8 m/s^2
normal_force = 588 N

distance = height / sin(angle)
distance = 2.50 m / sin(35 degrees)
distance = 4.28 m

force_friction = coefficient_friction * normal_force
force_friction = 0.0800 * 588 N
force_friction = 47 N

Work_friction = force_friction * distance
Work_friction = 47 N * 4.28 m
Work_friction = 201.16 J

Step 2: Calculate the work done against gravity during the climb.

The work done against gravity can be calculated using the formula:

Work_gravity = force_gravity * distance

The force of gravity can be calculated using the equation:

force_gravity = weight * sin(angle)

where the weight is equal to the mass multiplied by the acceleration due to gravity.

force_gravity = mass * gravity * sin(angle)
force_gravity = 60.0 kg * 9.8 m/s^2 * sin(35 degrees)
force_gravity = 325.08 N

Work_gravity = force_gravity * distance
Work_gravity = 325.08 N * 4.28 m
Work_gravity = 1391.42 J

Step 3: Use the work-energy principle to find the change in kinetic energy.

According to the work-energy principle, the work done by all forces acting on an object is equal to its change in kinetic energy.

The change in kinetic energy can be calculated using the formula:

Change_in_kinetic_energy = Work_friction + Work_gravity

Change_in_kinetic_energy = 201.16 J + 1391.42 J
Change_in_kinetic_energy = 1592.58 J

Step 4: Calculate the final speed.

The change in kinetic energy equals the final kinetic energy minus the initial kinetic energy:

Change_in_kinetic_energy = (1/2) * mass * (final_speed^2 - initial_speed^2)

Solving for the final speed:

1592.58 J = (1/2) * 60.0 kg * (final_speed^2 - 12.0 m/s)^2

2 * 1592.58 J = 60.0 kg * (final_speed^2 - 12.0 m/s)^2

3185.16 J = 60.0 kg * (final_speed^2 - 144.0 m/s^2)

Divide both sides by 60.0 kg:

53.085 m^2/s^2 = final_speed^2 - 144.0 m/s^2

Add 144.0 m/s^2 to both sides:

final_speed^2 = 197.085 m/s^2

Take the square root of both sides to find the final speed:

final_speed = sqrt(197.085 m/s^2)
final_speed = 14.04 m/s (rounded to two decimal places)

Therefore, the skier's final speed at the top of the 2.50-m rise is approximately 14.04 m/s.

To find the final speed of the skier at the top of the incline, we need to consider the conservation of mechanical energy.

First, let's find the potential energy (PE) at the top of the incline, using the formula:
PE = m * g * h

Where:
m = mass of the skier = 60.0 kg
g = acceleration due to gravity = 9.8 m/s^2
h = height of the incline = 2.50 m

PE = 60.0 kg * 9.8 m/s^2 * 2.50 m = 1470 J

Next, let's calculate the initial kinetic energy (KEi) of the skier using the formula:
KEi = 0.5 * m * v^2

Where:
m = mass of the skier = 60.0 kg
v = initial velocity = 12.0 m/s

KEi = 0.5 * 60.0 kg * (12.0 m/s)^2 = 4320 J

Now, we need to find the work done against friction (Wfriction) as the skier moves up the incline. The work done against friction is given by the equation:
Wfriction = f * d * cos(angle)

Where:
f = force of friction = coefficient of friction * Normal force
d = distance moved up the incline
angle = angle of the incline = 35 degrees

The normal force (N) is equal to the weight of the skier, which is given by:
N = m * g

N = 60.0 kg * 9.8 m/s^2 = 588 N

Now, let's calculate the force of friction (f):
f = coefficient of friction * Normal force
f = 0.0800 * 588 N = 47.04 N

To find the distance moved up the incline (d), we can use trigonometry. The distance moved up the incline is the vertical distance (h) divided by the sine of the angle:
d = h / sin(angle)

d = 2.50 m / sin(35 degrees) = 4.35 m

Substituting these values into the equation for work done against friction:
Wfriction = 47.04 N * 4.35 m * cos(35 degrees) = 181.4 J

Since work done against friction is always negative (as it opposes motion), we can rewrite this as:
Wfriction = -181.4 J

Now, let's apply the conservation of mechanical energy:
KEi + PE + Wfriction = KEf

Where KEf is the final kinetic energy at the top of the incline.

Rearranging the equation:
KEf = KEi + PE + Wfriction

KEf = 4320 J + 1470 J - 181.4 J = 5608.6 J

Finally, we can find the final speed (vf) by using the equation for kinetic energy:
KEf = 0.5 * m * vf^2

Rearranging the equation and solving for vf:
vf = sqrt(2 * KEf / m)

vf = sqrt(2 * 5608.6 J / 60.0 kg) = 10.1 m/s

Therefore, the skier's final speed at the top of the incline is 10.1 m/s.

Wt. = Fg = m*g = 60kg * 9.8N/kg=588 N.=

Wt. of skier.

Fp=588*sin35 = 337 N.=Force parallel to
incline.
Fv = 588*cos35 = 482 N. = Force perpendicular to incline.

Fk = u*Fv = 0.08 * 482 = 38.5 N. = Force
of kinetic friction.
d =h/sinA = 2.5/sin35 = 4.36 m.

Ek + Ep = Ekmax - Fk*d
Ek = Ekmax-Ep-Fk*d
Ek=0.5*60*12^2-588*2.5-38.5*4.36=2682 J.
Ek = 0.5m*V^2 = 2682 J.
30*V^2 = 2682
V^2 = 89.4
V = 9.5 m/s = Final velocity.