|V| = 10.33 units and the direction θ = -47.35° or 312.65°.
Given the x and y components of a vector, we can calculate the magnitude and direction from these components.
Applying the Pythagorean theorem we have that the magnitude of the vector is:
|V| =
|V| =
The expression for the direction of a vector comes from the definition of the tangent of an angle:
tan θ = ------> θ = arc tan
θ = arc tan
θ = -47.35° or 312.65°
(a) 0.74 m/s^2
Explanation:
There are two forces acting on the skier: the component of the weight parallel to the slope, which acts downward, and the frictional force, which acts upward along the incline.
The component of the weight parallel to the inclined plane is:
where m is the mass of the skier, and
.
The frictional force is instead
is the coefficient of friction for waxed wood on wet snow.
If we apply Newton's second law, we can write that the net force must be equal to the product of mass per acceleration:
And symplifying m, we can find the acceleration:
(b)
Explanation:
This time, the skier is moving at constant velocity. Therefore, the acceleration is zero (a=0) and Newton's second law becomes:
By simplifying, we get
From which we can find the angle at which the skier could coast at a constant velocity: