If a skier wants to slide down a slope at a constant speed with a coefficient of kinetic friction of 0.05, what angle should he choose?

To determine the appropriate angle for the skier to slide down the slope at a constant speed, we need to consider the forces acting on the skier. When the skier is moving at a constant speed, the net force acting on them is zero. This means that the force due to gravity acting down the slope must be balanced by the frictional force acting up the slope.

The force due to gravity can be expressed as ( mg \sin(\theta) ), where ( m ) is the mass of the skier, ( g ) is the acceleration due to gravity, and ( \theta ) is the angle of the slope. The frictional force is given by ( f_f = \mu_k N ), where ( \mu_k ) is the coefficient of kinetic friction and ( N ) is the normal force. The normal force can be determined as ( N = mg \cos(\theta) ).

The frictional force can, therefore, be expressed as ( f_f = \mu_k mg \cos(\theta) ).

Setting the gravitational force down the slope equal to the frictional force, we have:

[ mg \sin(\theta) = \mu_k m g \cos(\theta) ]

By simplifying