PHYSICS HELP - velocity & vectors?

Question

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PLEASE EXPLAIN BRIEFLY AND LABEL ANSWERS!
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A helium balloon rises upward at rate of 7.0 metres/second, to a height of 20 m before it pops. A steady breeze of 1.5 m/s due east blows against the balloon.

A) What is the velocity of the balloon relative to the ground?

B) How long does it rise before popping?

C) How far from its starting point has it flown (final displacement)?

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A firefighter climbs up 10.0 m ladder leaning against a vertical wall. The ladder makes an angle of 20 degrees with the wall. The firefighter reaches the roof in 15.0 s.

A) What is the height of the wall?

B) How far is the base of the ladder from the wall?

C) What is the firefighter's average vertical velocity?

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Suzanne is skiing with a velocity of 18.0 m/s [N30.0 degrees W]. What is the [N] component of her velocity vector?

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Tim is running cross-country at 6.4 m/s [S] when he completes a wide turn and continues at 5.8 m/s [W]. What is his change in velocity?

Answer 1

Balloon
A) The balloon's horizontal component of velocity quickly matches the wind speed. So you need to add perpendicular vectors. Add the 7.0 metres/second vertical and the 1.5 m/s due east. The magnitude of the resultant velocity is the hypotenuse of a right triangle with the 2 perpedicular sides being 7 versus 1.5. I hope you can handle the vector math if you're getting problems like this.

B) Supposedly it starts from the ground with a vertical velocity of 7 m/s right from the start -- no acceleration. So use
v = y/t
where v is 7 m/s and y is 20 m.

C) Use
v = y/t
where v is the magnitude of the resultant found for part A and t is from B.

Firefighter
A) Hmm, it doesn't say, do you think the ladder reached the top of the wall? It could be that the ladder only reaches halfway up the wall. But I don't see a way to calculate wall height without assuming it reaches the top. The 10 m ladder is the hypotenuse.
cos20 = y / 10 m should do it

B) sin20 = x / 10 m

C) Vv = y / t
where y is from A and t = 15 s.

Skiing
These are really just trig. Her velocity has a northward component and a westward component. Her 18.0 m/s velocity is the hypotenuse. Try cos.

X-country
I'm not sure how they mean that. Perhaps you could say the change is -0.6 m/s and 90 degrees to the right.