What is the distance and direction between city A and city C?

  • Thread starter Thread starter hrgardner33
  • Start date Start date
  • Tags Tags
    Vectors
AI Thread Summary
To determine the distance and direction from city A to city C, an airplane flies 200 km due west to city B and then 345 km at an angle of 34.5° north of west to city C. The solution involves using the Pythagorean theorem, but since the triangle formed is not right-angled, sine and cosine functions are necessary to find the lengths of the sides. The angle of 34.5° is interpreted as a clockwise rotation from the negative x-axis (west). Ultimately, the calculated straight-line distance from city A to city C is approximately 398.78 km.
hrgardner33
Messages
2
Reaction score
0

Homework Statement



An airplane flies 200 km due west from city A to city B and then 345 km in the direction of 34.5° north of west from city B to city C. In straight-line distance, how far is city C from city A? Relative to city A, in what direction is city C?


Homework Equations



The Pythagorean theorem


The Attempt at a Solution



398.78 km
 
Physics news on Phys.org


The Pythagorean theorem is about right-angled triangles. The triangle ABC in your problem is not right-angled.

The way to solve this would be: draw the situation, then try to make some right-angled triangle, calculate the length of its sides using sine and cosine functions and then use the Pythagorean theorem.
 


I don't know how to draw 34.5 degrees north of west.
 


Yeah I can understand that, I do not find it very clear terminology either, but I am assuming they meant rotating the negative x-axis (i.e. west) 34.5 degrees in clockwise direction (i.e. towards north).
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
View full post »

Similar threads

How Can Understanding Displacement vs. Distance Help Solve Physics Problems?
Replies
1
Views
7K
Vectors: Displacement, average velocity & speed
Replies
7
Views
2K
Frames of Reference Question - Airplane Problem
Replies
3
Views
3K
Optimizing Airplane Direction in Windy Conditions
Replies
3
Views
2K
Kinematics Question -- Plane heading to take into a headwind
Replies
7
Views
2K
Solve Hard Vector Problem: Location of City C
Replies
2
Views
6K
How Do You Calculate Direction and Vector Components in Physics Problems?
Replies
3
Views
3K
Distance & Direction City A to City C - Vector Question HELP
Replies
17
Views
5K
Archived Special relativity: train between two cities
Replies
1
Views
2K
Plane Traveling against the wind
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top