Kim and Kent are on opposite sides of a canal, pulling a barge with tow ropes. Kim exerts a force of 50N at 20 degrees to the canal and Kent pulls at an angle of 15 degrees with just enough force so that the resultant force vector is directly along the canal. Find the number of Newtons with which Kent must pull and the magnitude of the resultant vector.

Question

Kim and Kent are on opposite sides of a canal, pulling a barge with tow ropes.  Kim exerts a force of 50N at 20 degrees to the canal and Kent pulls at an angle of 15 degrees with just enough force so that the resultant force vector is directly along the canal.  Find the number of Newtons with which Kent must pull and the magnitude of the resultant vector.

Steve · Answer

Draw a diagram. Let the barge be in the canal, with Kim on the south shore, and Kent on the north shore, both pulling eastward. Then we have

Kim: u = <50cos20,-50sin20>
u = <46.98,-17.10>

Kent: v = <kcos15,ksin15>
= <0.966k,0.259k>

You want the resultant u+v to point eastward, so

-17.10 + 0.259k = 0
k = 66.02

So, Kent pulls with a force of 66 N.

u+v = <46.98+63.78,0> = <110.76,0>