Static friction problem for person to walk up plank

[Hyperfluxe]

Homework Statement

Homework Equations

See my work.

The Attempt at a Solution

 

[Xisune]

You used the wrong trig function, you multiply all forces by sin40 except for friction going up, that's when you use cos40 .

 

[Hyperfluxe]

Shouldn't the weights be multiplied by cos(40) because they are vertically downwards, so the moment arm would be the horizontal distance?

 

[Xisune]

Shouldn't the weights be multiplied by cos(40) because they are vertically downwards, so the moment arm would be the horizontal distance?

You're right, my mistake.

The answer I get still doesn't match yours, but I can barely see the text, do you have a clearer picture of the solution?

 

[Hyperfluxe]

Yeah my bad, the quality is horrendous. Here's a way better one:

 

[Xisune]

You used the wrong equation during the final step. Set 165.22s + 70.81 equal to equation 2. That should get you the correct answer.

 

[Hyperfluxe]

Wow that was such a silly mistake haha. Thanks for pointing it out! I got 1.00m as the answer.