EK Physics Lecture 1 questions

[orthoboy]

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[vayntraubinator]

Okay I am having trouble with two questions in the First lecture in the EK Physics book.

#1) A weather balloon travels upward for 6 km while the wind blows it 10 km north and 8 km east. Approximately what is its final displacement from its initial position?

A) 7 km
B) 10 km
C) 14 km
D) 20 km

I honestly don't get what the answer explanation is trying to say.

Think of an x, y, z axis. The wind blows the balloon up the y axis 6 km. Then blows the balloon down the z axis for 10 km and 8km down the x axis.

Now, imagine where it's final position is...it shows this in the solution.

The math is a bit tricky but simple if you understand whats going on.

Since these are two right triangles, visualize the third right triangle from the origin of the x,y, and z axis.

This hypotenuse you can get by taking the square root of 6^2 + 8^2+10^2
That sum is 200. The square root of 2 is ~ 1.41, so multiply by 10(factored out the square root of 100) and you get 14.1m.

Or C

#3) A man entered a cave and walked 100 m north. He then made a sharp turn 150 degrees to the west and walked 87 m straight ahead. How far is the man from where he entered the cave?

This one I don't get what 150 degrees to the west means and how does this make a 30/60/90 triangle?

Picture a Big arrow pointing north now with a length of 100m.

Now, from north, rotate 150 degrees downward. We are rotating from an angle of 90 degrees already, so the total angle from the right x axis is 240 degrees. The side of the y axis going downward is at the angle 90(3)=270 degrees, so we can see that 270-240 = 30 degrees. If you have trouble visualizing that.

Now, they tell you that 100cos30=87. Since that is the length we walked in that direction, to find the opposite side, we just do 100sin(30) and this is .5 on the 30/60/90 triangle. Hence, .5(100) = 50meters. B