Question

A skier slides down a slope with 12 degrees below horizontal. Ignoring friction and air resistance, the skier's acceleration is most nearly: a) 0 b) 2m/s2 c) 5m/s2 d) 8m/s2 e) 10m/s2

Answer 1

The acceleration of a skier sliding down a 12-degree slope is most nearly 2 m/s², calculated by taking the sine of the slope angle (12 degrees) and multiplying it by the acceleration due to gravity.

Step-by-step explanation:

The student is asking about the acceleration of a skier sliding down a slope that is inclined 12 degrees below the horizontal. To answer this question, we will refer to basic physics principles concerning motion on an inclined plane without considering the effects of friction and air resistance. The acceleration of an object sliding down an incline can be determined by using the component of gravitational acceleration (g) that is parallel to the slope. The gravitational acceleration is approximately 9.8 m/s2 on Earth.

To find the acceleration component parallel to the slope (a), we use the formula:

a = g × sin(θ)

Where:

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θ is the angle of the slope relative to the horizontal plane (12 degrees)

Substituting the values into the formula gives us:

a = 9.8 m/s2 × sin(12°) ≈ 9.8 m/s2 × 0.2079

Which yields:

a ≈ 2.04 m/s2

Therefore, the skier's acceleration is most nearly 2 m/s2 (option b).

Answer 2

The acceleration is zero (0)

Step-by-step explanation:

The fact that the skier is moving and does not receive any kind of force that reduces or increases its speed allows us to understand that it is moving at a constant velocity and when anybody moves at constant velocity the acceleration is zero.

this is explained and understood mathematically by the interpretation of newton's second law which plasma in the following equation:

`F=m*a\\where:\\\\F = sum of forces [N]\\m = mass of the body [kg]\\a = acceleration of the body [m/s^(2)]\\`

If there are no forces acting over the body:

`0= m* a\\a=(0)/(m) \\a=0`