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A truck undergoes two consecutive displacements, the first is 75 km due 30.0 degrees west of north, and the second is 155 km due 60.0 degrees due east of north. What is the total displacement of the truck?

User Ekans
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1 Answer

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here we need to write the two components of the displacement and then we need to add them

first displacement is given as


d_1 = 75 km 30 degree West of North


d_1 = - 75 sin30 \hat i + 75 cos 30 \hat j


d_1 = - 37.5 \hat i + 64.9\hat j

Other displacement is given as


d_2 = 155 km 60 degree due East of North


d_2 = 155 sin60 \hat i + 155 cos60 \hat j


d_2 = 134.2 \hat i + 77.5 \hat j

now we need to find the net displacement


d = d_1 + d_2


d = (-37.5 + 134.2)\hat i + (64.9 + 77.5)\hat j


d = 96.7\hat i + 142.4\hat j

so it is given as


d = √(96.7^2 + 142.4^2)


d = 172.1 km

and its direction is given as


\theta = tan^(-1)(96.7)/(142.4) = 34.1 degree

so it will displace by 172.1 km at 34.1 Degree East of North

User WestHamster
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