Question

A delivery truck starts it’s run by driving 5.20 km due west before turning due north and driving an additional 2.10 km. Finally, the truck turns 30.0 degrees north of east and drives for 3.70 km before reaching its first dropoff point. What is the magnitude of the total displacement of the truck from where it started to its first dropoff point?

Answer 1

4.427 m

Step-by-step explanation:

We shall consider east as + x- axes and north as + ve y- axes. .

We shall represent every displacement in vector form as follows

D₁ = 5.2 km due west = - 5.2 i

D₂ = 2.1 km due north = 2.1 j

D₃ = 3.7 km towards north east at 30 degree from east

= 3.7 cos30 i + 3.7 sin 30 j = 3.2 i + 1.85 j

Total displacement D = D₁ + D₂ +D₃ +D₄.

- 5.2 i + 2.1 j + 3.2 i + 1.85 j

= - 2 i + 3.95 j

Magnitude of D

D² = (2)² + (3.95)²

= 4 + 15.6025

D = 4.427 m