Physics Contest Question!

[whoareyou]

A pilot flew his airplane at a constant altitude and uniform speed v due east for a time t. He turned left through an angle θ, without changing speed or altitude, and flew for an equal time t. The magnitude of his displacement from his starting point after the first leg of the flight was the same as the magnitude of his displacement from his starting point after the second leg of the flight. What was the measure of the angle θ?

[Zren]

Vector has both magnitude and direction.

Draw it.


The second part can be anywhere from 0 -> 180 degree turn (otherwise it'd probably be a right turn).

So at what angle for the angle ABC does the magnitude from AB equal the mangitude of AC?

[whoareyou]

Would you have to use the sine law?

And I know that the correct answer for this problem is 120degrees, but I was just not sure how to proceed.

When dealing with these types of problems, I learned to use to break up the vectors into components ... will that work for this case?

[Zren]

Oh you do?

Well.


Since it's a 120 degree turn. That means the angle ABC is 60. And since both lines are equal, it's an isoceles triangle.

... which leads to it being a....?

Like I said, draw it. :]

[apython1992]

hooray physics!

[whoareyou]

I have absolutely no idea ... :O

[Zren]

The distance traveled between the two parts of the flight are equal, as is the distance from the starting point to the final point.

All equal.

A triangle with 3 equal sides.

Since you know that, then the angles must be...

*cough* http://www.mathsisfun.com/triangle.html *cough*

Look for commonly known triangles in physics as most books tend to use them. You should at least remeber the
45-45-90: http://en.wikipedia.org/wiki/File:45-45-triangle.svg
30-60-90: http://en.wikipedia.org/wiki/File:30-60-90.svg

[whoareyou]

OMG! I feel so dumb now!

This question was actually taken from the OAPT 2010 Physics Contest.

I'm preparing for the 2011 one.

Although, since this is a computer science forum, I don't think I should be posting anymore problems that I have.

[apython1992]

No, by all means do! Many people here from what I can tell are interested in Physics, and any questions of this sort could go into general discussion, student life, or even off-topic if you feel like you're really stretching. I know I'd be glad to talk about physics too.

[Sur_real]

Ahhh physics contests...
This reminds me, I don't even know why I signed up for SIN o well >.>

[apython1992]

My high school physics textbook had a lot of SIN questions in them, I really enjoyed those ones. I wish I knew more about contests when I was in high school.

[A.J]

I remember the year when a friend of mine form school and I got invited to POPTOR. That year they only considered the CAP exam for National Camp, and as a result we didn't get invited to National camp. I hope things are different now.

[whoareyou]

WOW! A lot of people seem interested in physics here.

Well then, since I may need help practicing for my physics competition, I will make a new thread dedicated to it.

If I need help, I'll ask there!

[andrew.]

My grade 12 physics teacher used to use old SIN questions for our assignments and tests (and even the exam).