Question

find the magnitude and direction of force 40N and 20N at a point if the angle between forces is 60°​

Answer 1

As a general case, consider two vectors P⃗ and Q⃗ of magnitude P and Q respectively with an angle θ between them.

Then, the magnitude, R , of the resultant vector R⃗ and its angle, α, with vector P⃗ are given by,

R=P2+2PQcosθ+Q2−−−−−−−−−−−−−−−−−√ and

α=arctan(QsinθP+Qcosθ).

In this case, P=15N,Q=20N and θ=60o.

Hence, R=152+2(15)(20)cos60o+202−−−−−−−−−−−−−−−−−−−−−−−√=925−−−√=537−−√N.

And α=arctan(20sin60o15+20cos60o)=arctan(23√5)≈40.8934o.

So, the resultant force has a magnitude of 537−−√N and makes an angle of 40.8934o with the vector of magnitude 15N .

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