Question

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?

Answer 1

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