# physics

posted by .

A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.

• physics -

You can just use basic Trig a few times.

First, find x1 and y1 (I’m defining these as the x and y components of the first triangle, the one where a is the hypotenuse. I drew them in green in the diagram above).

x1 = 175*cos(30)
y1 = 175*sin(30)

You can do the same thing for the next triangle, where 150 is the hypotenuse. I’ll call the components x2 and y2. (This triangle is orange.)

x2 = 150*sin(20)
y2= 150*cos(20)

(Note that because of the orientation of this triangle, you have the rare case where the horizontal component is sine, and the vertical component is cosine.)

Now I’m going to define a new point, let’s call it Z. This is the point between C and B where the line crosses the y-axis. If you want to find CO, you first need to find CZ and ZO. You now have everything to do this.

CZ = 190 – (x1-x2) [draw some dotted lines across the triangles to see why this is]
CZ = 190 – (175*cos(30) – 150*sin(20))
CZ = 89.75

OZ = y1 + y2
OZ = 175*sin(30) + 150*cos(20)
OZ = 228.45

Now you can find CO by using Pythagorean Theorem.

CO^2 = CZ^2 + OZ^2
CO^2 = 89.75^2 + 228.45^2
CO = 245

Lastly, you need to find the angle. You just use Trig to do this.

So the new position is 245 km away, 21.5 degrees West of North.

## Similar Questions

1. ### ALGEBRA 2

A plane takes off from an aiport and flies east at a speed of 350 mi/h. Ten minutes later, a second plane takes off from the same airport and flies east at a higher altitude at a speed of 400 mi/h. How long does it take the second …
2. ### science

a commuter plane starts from an airport and takes the route whereby it starts to city,located 175km away in a directiin 30egrees north of east of east. Next, it flies for 150 km 20degrees west of north,to city b.finally, the plane …
3. ### Physics

A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to …
4. ### physics

A plane flies from base camp to Lake A, 220 km away in the direction 20.0° north of east. After dropping off supplies it flies to Lake B, which is 150 km at 30.0° west of north from Lake A. Graphically determine the distance and …
5. ### physics

A regional airline flight consists of two legs with an intermediate stop. The airplane flies 380 due north from airport A to airport B. From there, it flies 260 due east to its final destination at airport C. Part A What is the magnitude …
6. ### Physicis

Airplane staring from airport a flies 300 km east then 395 km 26.5 degrees west of north, and then 150 km north to arrive at airport b. what angle is the straight flight from a to b north of east and how far
7. ### Math

A plane flies due east for 120 km from airport a to airport b it then flies due north for 280 km to airport c finally it flies directly back to airport a calculate the direct distance from airport to airport a give your answer to the …
8. ### Algebra

A plane takes off from an airport and flies east at a speed of 350 mph. Ten minutes later, a second plane takes off from the same airport and flies east at a higher altitude at a speed of 400 mph. How long does it take the the second …
9. ### physics vectors

A plane flies from base camp to Lake A, 260 km away in the direction 20.0° north of east. After dropping off supplies it flies to Lake B, which is 150 km at 30.0° west of north from Lake A. Graphically determine the distance and …
10. ### physics

A plane flies from base camp to Lake A, 260 km away in the direction 20.0° north of east. After dropping off supplies it flies to Lake B, which is 150 km at 30.0° west of north from Lake A. Graphically determine the distance and …

More Similar Questions