# Find magnitude and direction of resultant of three given forces?

Using this diagram:

A hot-air balloon is ready for take-off. The diagram shows the balloon, tethered by two ropes AB and CD, reach attached to the balloon and the horizontal ground. The weight of the balloon is 3000N. The tensions in AB and CD are 250N and 100N respectively. AB and CD make angels of $60°$ and $30°$ respectively with the vertical.

(i) By modelling the balloon as a particle, find the magnitude and direction of the resultant of the three given forces on the balloon.

Can anyone please point me in the correct direction?

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rx=86.60 ry=50 ${}{}{}{}{}{}{}{}{}{}{}$ –  user85226 Jul 6 '13 at 13:05

## 1 Answer

You need to add the three vectors to find the single vector that is the equivalent.

One way to do this is to replace each individual vector with two components, one in the vertical direction and one in the horizontal direction. You can then add all the horizontal components to give one net horizontal component, and the same for the vertical components. If you use the angles as shown in the diagram, be sure to pay attention to whether the components are up or down, or left or right.

For example, for the force CD:

$$F_{down} =100 cos(30)$$ $$F_{left} =100 sin(30)$$

Lastly, the two net components can be re-combined into one vector with a single size and direction.

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