Solving Simple Work Problem: 515J

[Mr Davis 97]

Homework Statement

A 70.0 kg sailor climbs an 11.5 m long rope ladder to a mast above at constant velocity. The rope ladder is at an angle of 30.0° with the mast. Assume that the ladder is frictionless. How much work does the sailor do?

Homework Equations

$W = Fd$

The Attempt at a Solution

[/B]
$F_{net||} = F_{a} + F_{g||}$
$F_{a} = -F_{g} = -mg\sin \theta$
$W = F_{a}d$
$W = -mgd\sin \theta$
$W = -(70kg)(-9.8m/s^{2})(11.5m)0.5$
$W = 515 J$

However, in the solution manual, this is not the correct answer. What am I doing wrong?

 

[SammyS]

Homework Statement

A 70.0 kg sailor climbs an 11.5 m long rope ladder to a mast above at constant velocity. The rope ladder is at an angle of 30.0° with the mast. Assume that the ladder is frictionless. How much work does the sailor do?

Homework Equations

$W = Fd$

The Attempt at a Solution

[/B]
$F_{net||} = F_{a} + F_{g||}$
$F_{a} = -F_{g} = -mg\sin \theta$
$W = F_{a}d$
$W = -mgd\sin \theta$
$W = -(70kg)(-9.8m/s^{2})(11.5m)0.5$
$W = 515 J$

However, in the solution manual, this is not the correct answer. What am I doing wrong?

The angle, θ, that you used is with respect to the deck, so it's not 30° .

That is to say, if you use sin(θ) that is with respect to the deck.