College Physics

Question

Two airplanes leave an airport at the same
time. The velocity of the first airplane is
700 m/h at a heading of 11.6
◦
. The velocity
of the second is 560 m/h at a heading of 127◦
.
How far apart are they after 3 h?
Answer in units of m.

Answer 1

Pane 1:

 

x₁ = (v cosθ)t

y₁ = (v sinθ)t

 

Plane 2:

 

x₂ = (u cosφ)t
y₂ = (u sinφ)t

 

Plug in

 

v = 700

θ = 11.6º

u = 560

φ = 127°

t = 3

 

and get x₁, y₁, x₂, and y₂ in units of m.  Then use the distance formula to find the distance from (x₁,y₁) to (x₂,y₂).

 

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

 

Pug in the numbers and get d in units of m.  You can finish from here.