- #1

bearjew11

- 4

- 0

**The figure shows the successive displacements of an aircraft flying a search pattern. The initial position of the aircraft is P and the final position is P'. What is the net displacement (magnitude and direction) between P and P'?**

**My attempt:**

So, my understanding is that the net displacement of the successive displacement vectors is the overall sum of the successive displacement vectors. (?)

Also, referring to the rules of alternate interior angles, ∠A, ∠B, and ∠C = 60° (?)

ΔA

Hypotenuse = 18km

Height = 18sin60°

Base = 18cos60°

ΔB

Hypotenuse = 9.5km

Height = 9.5sin60°

Base = 9.5cos60°

ΔC

Hypotenuse = 12km

Height = 12sin60°

Base = 12cos60°

My attempt to find the base of the triangle formed by the point P and P' and the x-axis was to add the bases of ΔA and ΔB and subtract the base of ΔC from the sum.

With my calculations (using rounded decimals and plugging in the exact values):

I got ~13km for →P (incorrect because my book reads 11.2km)

and for ∠θ I got 57.1° (incorrect, because the remaining angle should be 27.7° and is 32.9° with my calculations)

I am doing something wrong. HELP