Question

A boat sails south with the help of a wind blowing in the direction \({\rm{S}}{36^\circ }{\rm{E}}\) with magnitude 400 lb. Find the work done by the wind as the boat moves \(120{\rm{ft}}\).

Short answer

The work done is \(38,832ft - lb\).

Step-by-step solution

Formula used to find the work done

The expression to find the work done\((W)\):

\(W = |{\rm{F}}||{\rm{D}}|\cos \theta \) …… (1)

Here,

F Force,

D is the displacement vector, and

\(\theta \)is the angle between \({\rm{F}}\) and \({\rm{D}}\).

Calculation to find the work done

Given:

\(|{\rm{F}}| = 400{\rm{lb}},\theta = {36^\circ }\) and \(|{\rm{D}}| = 120{\rm{ft}}\)

In equation (1), substitute \(400{\rm{lb}}\) for\(|{\rm{F}}|\), \(120{\rm{ft}}\) for \(|{\rm{D}}|\) and \({36^\circ }\) for\(\theta \).

\(\begin{aligned}{l}W &= (400lb)(120ft)\cos \left( {{{36}^\circ }} \right)\\ &= (400lb)(120ft)(0.809)\\ &= 38,832ft - lb\end{aligned}\)

Thus, the work done is \(38,832ft - lb\).