Hi, I am having trouble solving the following problem: "A weather balloon travels upward for 6 km while the wind blows it 10 km north and 8 km east. Approximately what is the final displacement from its initial position?" I am not understanding how to draw a vector diagram to solve this problem...any suggestions as to how I can tackle problems such as these? Thank you.

If I'm not mistaking... it's a vector summation problem. Best thing to do is to draw the picture adding the vectors from head to tail. then go on from there

Here, upward is the same as north. So the weather balloon itself travels 6 km north. The wind then pushes it 10 more km north and then 8 km to the east (right). If you draw it out on paper you should get a right angled triangle with one side of 16 km and the other of 8 km. Now just apply the Pythagorean theorem to find the length of the hypotenuse and that's your displacement.

Is this a trick question? I read upwards as Z axis. So the balloon is moving along all 3 axis x,y & z. So in this case the solution would be the vector sum (S1) in the x & y (S1=x+y) and then the vector sum S1 & z (S1+z). Its confusing on what they mean though. Do you know the answer(a,b,cd options)?

Sorry, I misinterpreted. Just because it's a weather balloon, it would be logical to assume upward equals z-axis. The same Pythagorean theorem would apply though according to the vector sums of the poster above.