Vectors, Components, Motion, and Relative Velocity

1) the rectangular and polar coordinates of a point are(x,y) and (r,θ), where x=6 and θ =27 degrees. Find value of r and value of y.

2) Assume the water has uniform velocity represented by the vector Q in the diagram below. The shore lines are on the left and right hand side of the diagram. A river is crossed by a girl rowing a boat. The rowing speed of the girls's boat and a set of possible orientations of her boat(relative to still water) are shown in the diagram.

(see attachment)

For an observer on shore, the speed of the boat for direction H is > than for direction W.
a) true
b) false

3) To land directly across the river, she must row in direction Y.
a) true
b) false

4) To get across the river in the shortest time, she must row in direction Y.
a) true
b) false

5) Time to row across for direction H is equal to that for direction P.
a) true
b) false

6) Time to row across for direction Y is less that for direction P.
a) true
c) false

7) The total distance traveled in crossing for direction P is greater that for direction H.
a) true
b) false

A humming bird flies 2.1m along a straight path at a height of 3.5m above the ground. Upon spotting a flower below, the hummingbird drops directly downward 2.8m to hover in front of the flower.

a) What is the magnitude of the hummingbird's total displacement? Answer in units of m.
b) How many degrees below the horizontal is this total displacement? Answer in degrees.

8) A plane travels 3.8km at an angle of 26 degrees to the ground, then changes direction and travels 7.4km at an angle of 13 degrees to the ground.

a) What is the magnitude of the plane's total displacement? Answer in km.
b) At what angle above the horizontal is the plane's total displacement? Answer in degrees.

9) The pilot of an aircraft wishes to fly due west in a 48.6km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 174 km/h.

a) How many degrees from west should the aircraft head? Let clockwise be positive. Answer in degrees.
b) What should the planes speed be relative to the ground? Answer in units of km/h.
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