A skier slides horizontally along the snow for a distance of 12.1 m before coming to rest. The coefficient of kinetic friction between the skier and the snow is 0.0343. Initially, how fast was the skier going?

a = u*g = 0.0343 * (-9.8) = -0.336 m/s^2.

V^2 = Vo^2 + 2a*d = 0.
Vo^2 = -2a*d = -2*(-0.336)*12.1 = 8.13.
Vo = 2.85 m/s.

Well, let me slide right into this question for you! Given that the skier came to rest, we know that the kinetic energy was completely converted into friction. To find the initial speed, we can use the work-energy principle. The work done by friction is equal to the initial kinetic energy of the skier.

Now, the work done by friction is given by the formula: work = force x distance. In this case, the force of friction is the coefficient of kinetic friction multiplied by the normal force (which is equal to the weight of the skier).

To calculate the force of friction, we multiply the coefficient of kinetic friction by the weight of the skier. But since we know that the skier came to rest, the normal force and the weight must be equal.

Therefore, we can rewrite the work equation as: work = (coefficient of kinetic friction) x (weight of the skier) x distance.

Plugging in the given values, the work is equal to 0.0343 x (weight of the skier) x 12.1 m.

Now, the work done is equal to the initial kinetic energy, which is given by the formula: kinetic energy = (1/2) x (mass of the skier) x (initial velocity)^2.

Since the mass of the skier cancels out, solving for the initial velocity gives us: initial velocity = square root of ((2 x work) / (mass of the skier)).

However, we don't have the information about the mass of the skier. So unfortunately, we can't calculate the initial velocity. But hey, at least we did some math with a slippery twist!

To find the initial speed of the skier, we can use the concept of work-energy theorem. According to the work-energy theorem, the work done on an object is equal to the change in its kinetic energy. In this case, the work done on the skier is done by the force of friction. So, we can set up the equation:

Work done by friction = Change in kinetic energy

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

Work = force * distance

The force of friction can be found using the formula:

Force of friction = coefficient of friction * normal force

Since the skier is sliding horizontally, the normal force will be equal to the weight of the skier, which can be calculated using the formula:

Normal force = mass * acceleration due to gravity

Let's calculate the initial speed step-by-step:

Step 1: Find the weight of the skier.
- Assume the mass of the skier is M (unknown).
- The acceleration due to gravity is approximately 9.8 m/s².
- The weight of the skier can be calculated using the formula:

Weight = mass * acceleration due to gravity

Step 2: Calculate the normal force.
- The normal force is equal to the weight of the skier since the skier is sliding horizontally.

Step 3: Calculate the force of friction.
- The force of friction can be calculated using the formula:

Force of friction = coefficient of friction * normal force

Step 4: Calculate the work done by friction.
- The work done by friction can be calculated using the formula:

Work = force of friction * distance

Step 5: Calculate the change in kinetic energy.
- The change in kinetic energy is equal to the work done by friction.

Step 6: Calculate the initial speed.
- The initial speed can be found using the formula:

Initial kinetic energy = 1/2 * mass * initial velocity^2

Now, let's calculate each step:

Step 1:
Weight = M * 9.8 m/s²

Step 2:
Normal force = Weight

Step 3:
Force of friction = 0.0343 * Normal force

Step 4:
Work = force of friction * distance

Step 5:
Change in kinetic energy = Work

Step 6:
Initial kinetic energy = 1/2 * M * initial velocity^2

Since we have the distance, coefficient of friction, and the mass cancels out in the final equation, we can rewrite the equation as:

0.0343 * (M * 9.8 m/s²) * 12.1 m = 1/2 * M * initial velocity^2

Simplifying the equation:

0.334 * 118.8 = 0.5 * initial velocity^2

39.7272 = 0.5 * initial velocity^2

Dividing both sides by 0.5:

79.4544 = initial velocity^2

Taking the square root of both sides:

Initial velocity = √(79.4544)

Initial velocity ≈ 8.914 m/s

Therefore, the initial speed of the skier was approximately 8.914 m/s.

To find the initial speed of the skier, we need to use the equation for the work done by the force of friction, which is equal to the change in the skier's kinetic energy.

The work done by the force of friction can be calculated using the equation:

Work done by friction = force of friction * distance

The force of friction can be calculated using the equation:

Force of friction = coefficient of kinetic friction * normal force

The normal force is the force exerted by a surface to support the weight of an object resting on it. Since the skier is sliding horizontally, the normal force is equal to the skier's weight, which can be calculated using the equation:

Weight = mass * gravitational acceleration

The equation for the work done by the force of friction can now be written as:

Work done by friction = (coefficient of kinetic friction * mass * gravitational acceleration) * distance

We can rearrange this equation to solve for the skier's initial speed:

Initial speed = square root(2 * (coefficient of kinetic friction * mass * gravitational acceleration) * distance)

Now, we can substitute the given values into the equation to calculate the initial speed of the skier.