Emergency Landing

1. Aug 31, 2004

COCoNuT

Emergency Landing. A plane leaves the airport in Galisto and flies a distance 155 km at an angle 68.0 Degrees east of north and then changes direction to fly a distance 270 km at an angle 48.0 degrees south of east, after which it makes an immediate emergency landing in a pasture.

1.) When the airport sends out a rescue crew, how far should this crew fly to go directly to this plane? <--- know how to do this already and got the answer

2.) In which direction? (Express your answer as an angle measured south of east). <---- need help for this

ok i need help on #2, here's my work....

155cos(22)i +155sin(22)j
270sin(42)i +270cos(42)J

324.37i + 258.7j

arctan(y/x) = arctan(258.7/329.37) = 38 Degrees <--- my answer... What am i doing incorrectly? (please help within the next 5 hours if you can, that's when the hw is due). thanks

2. Aug 31, 2004

chroot

Staff Emeritus
How did you arrive at your second vector (270 sin 42, 270 cos 42)?

It seems to me it should be (270 cos -48, 270 sin -48).

- Warren

3. Sep 1, 2004

COCoNuT

155*cos(22) + 155sin(22)
270*cos(-48) + 270sin(-48)
-----------------------------
324.37 + (-142.58)

arctan (-142.58/324.37) = -24 Degrees south of east (answer must be in south of east)

is it ok to have a negative answer?

4. Sep 1, 2004

chroot

Staff Emeritus
Angles increase counterclockwise from the positive x-axis. Negative angles increase clockwise. -24 degrees is in the southeast quadrant. It's just 24 degrees south of east. Draw a picture if you don't see it.

- Warren

5. Sep 1, 2004

Sharayah

Helpppp

Hey... I am soo confused. What answer do you get so that I can see what the heck I am doing wrong?

6. Sep 1, 2004

chroot

Staff Emeritus
Sharayah,

It is our policy not to show explicit answers, but only provide a "path" the student might follow to solve the problem.

What exactly are you confused about? Have you been assigned the same question?

- Warren

7. Sep 1, 2004

Sharayah

Blah

I need help on the first question.

8. Sep 1, 2004

Sharayah

How do I approach it?

9. Sep 1, 2004

chroot

Staff Emeritus
Sharayah,

As we have explained already in this thread, break each vector into components, then add the components. The length of a vector (x1, x2) is

$$L = \sqrt{x_1^2 + x_2^2}$$

which is nothing more than the Pythagorean theorem.

- Warren

10. Sep 1, 2004

Sharayah

That is odd? I tryed that and ended up with the answer 307 km. Is that right? Ohh and sorry I barely came into the thread.

11. Sep 1, 2004

chroot

Staff Emeritus
Sharayah,

It doesn't seem to be correct. Please show me the steps you used to come up with 307 km.

- Warren

12. Sep 1, 2004

Sharayah

I took 155^2 and added 265^2.... then took the sqrt of that

In numerical terms sqrt(155^2+265^2)

13. Sep 1, 2004

chroot

Staff Emeritus
And where did you come up with the 155 and 265?

- Warren

14. Sep 1, 2004

Sharayah

Emergency Landing. A plane leaves the airport in Galisto and flies a distance 155 at an angle 68.0 east of north and then changes direction to fly a distance 265 at an angle 48.0 south of east, after which it makes an immediate emergency landing in a pasture.

15. Sep 1, 2004

Sharayah

Aren't those my two x distances?

16. Sep 1, 2004

chroot

Staff Emeritus
The problem posted originally had 270 km as the magnitude of the second vector, not 265 km.

What makes you think you can just add the lengths of the vectors in the way you suggested? As I explained, you need to break the vectors into components and then add the components to find the sum of the vectors. Do you know how to do this?

- Warren

17. Sep 1, 2004

needhelpperson

x(crew) = sin68*155+cos48*270
y(crew = cos68*155-sin48*270

took arctan(x/y) and got 23.7.. degrees south of east

18. Sep 1, 2004

Sharayah

I am sorry... I do not know how... I am new in physics and have not had a math class in over 2 years... so I am a little lost... but I should get it.

19. Sep 1, 2004

chroot

Staff Emeritus
Do you know what it means to represent a vector in terms of its components?

- Warren

20. Sep 1, 2004

Sharayah

The components are the 'getting the sin and cos' right? If so I need a little guidence on how to determine wether or not it is cos or sin?!