Question

A snowboarder of mass 60 kg is at rest on
the top of a sand dune. The coefficients of
static and kinetic friction are 0.55 and 0.4675,
respectively.

60 kg
μk = 0.4675
μs = 0.55

What is the angle  the incline must exceed
so that the snowboarder starts sliding? The
acceleration of gravity is 9.8 m/s2 .
Answer in units of ◦.

I worked out the variables but don't know where to go from there.

Answer 1

M*g = 60 * 9.8 = 588 N.

Fp = 588*sin A. = Force parallel to the incline.

Fn = 588*Cos A = Normal force.

Fs = us*Fn = 0.55*(588*Cos A = 323.4*Cos A.

Fp-Fs = M*a.
588*sin A-323.4*Cos A = 60*0 = 0,
588*sin A = 323.4*Cos A,
Divide by 588:
sin A = 0.55*Cos A,
Divide by Cos A:
sin A/Cos A = 0.55,
sin A/Cos A = Tan A,
Tan A = 0.55, A = 28.8 Degrees.