Question

In x-y plane, a force 10 N acts at an angle $30^{0}$ to the positive direction of x axis. The force can be written as

Moderate

Solution

Let $\vec{F} = x \hat{i} + y \hat{j}$
Now $F = \sqrt{x^{2} + y^{2}} = 10$
$\Rightarrow x^{2} + y^{2} = 100$ --------(i)
$\tan 30^{0} = \frac{y}{x} \Rightarrow y = \frac{1}{\sqrt{3}} x$ ------(ii)
solving (i) and (ii)
y = 5 N, x = $5 \sqrt{3} N$

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