PHYSICS HELP - velocity & vectors?

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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 od 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?

PHYSICS HELP - velocity %26amp; vectors?
So many questions for one post...





1A)- Upward at 7.0m/s, east at 1.5m/s. That's a right triangle, and the velocity will be the hypotenuse, which will be





SQRT(a^2 + b^2) =


SQRT(7.0^2 + 1.5^2) =


SQRT(49 + 2.25) =


SQRT (51.25) =~7.159m/s speed, relative to the ground. As for the angle it makes with the ground, remember that definition of tangent is the opposite/adjacent, so the tangent of the angle with the ground is 7/1.5 = 4.666... so the angle itself is the arctan of that number, or 77.9 degrees. So the velocity is





7.159m/s, eastward, 77.9 degrees up





1B) - Simply 20m/7m/s = 20s/7 =~2.857s





1C) - 7.159m/s * 2.857s =~ 20.454m