Question

A blimp is travelling at a velocity of 22km/h [E] relative to the air. A wind is blowing from the north at an average velocity of 15km/h relative to the ground. Determine the velocity of the blimp relative to the ground.

Answer 1

Hi! Any ideas?

Answer 2

I was thinking of drawing a triangle like this. ^ Does that make sense?

Answer 3

It makes a lot of sense! :)

Answer 4

Alright so, next I find the side length of the hypotenuse?

Answer 5

Yep! And do you know why you're doing it?

Answer 6

Not at all... Why?

Answer 7

So I used the Pythagorean theorem, and got 26.6km/h for the hypotenuse. What now?

Answer 8

Haha, okay! Well, you have the wind going south, so you know. Because it is coming \(\sf from\) the north.

Okay, so you have the balloon, and it is going
1. with the wind
2. plus 22 km/h east

And the wind, compared to the ground, is 15 km/h south.
So, overall, the balloon is going 15 km/h south and 22 km/h east

Answer 9

You are learning vector addition, right? And I got the same number. :)

Answer 10

I think I am. So is 26.6km/h the answer?

Answer 11

Yep, but you have to know the direction!

When you do vector addition, you draw one of your vectors. The tail of the next vector should then meet the head of the previous vector. So if I draw the 22 km/h east vector, I'll add the 15 km/h south vector next.

Answer 12

And the "resultant" vector, what you get from adding them, is the vector that
starts where the first vector started
and
ends where the last vector ended.

Answer 13

So, that's how you got your triangle! And it is a right triangle (because south and east are perpendicular).

So you found the "magnitude" of the balloon's velocity. What would you say the direction is?

Answer 14

Southeast.

Answer 15

That's the answer.

Answer 16

Thank you, I appreciate it.

Answer 17

You're very welcome :)