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Pythogarean:   V2= Vx2 + Vy2

Vx= V cos (Ø)

Vy= Vsin (Ø)

Ø= tan-1(Vy/Vx)

VECTOR 3 PROBLEMS

Draw three different ways to add the three vectors to get a resultant: (From book Chapter 3 pgs 113-117)

23. A submarine dives 110 meters at an angle of 10 degrees below the horizontal. What are the horizontal and vertical components of the sub’s displacement? See Sample Problem 3B.

25. A golfer takes two putts to sink his ball in the hole once he is on the green. The first putt displaces the ball 6 m eat, and the second putt displaces it 5.4 m south. What displacement would put the ball in the hole on one putt? See Sample Problem 3A

27. A roller coaster travels 41.1 meters at an angle of 40 degrees above the horizontal. How far does it move horizontally and vertically? See Sample Problem 3B

29. A person walks 10 m east, 300 m south, 150 m at 30 degrees south of west, then 200 m at 60 degrees north of west. What is the person’s resultant displacement from the starting point? See Sample Problem 3C.

51. A river flows due east at 1.5 m/s. A boat crosses from the south shore to the north shore by maintaining a constant velocity of 10 m/s due north relative to the water.

a) What is the velocity of the boat as viewed by an observer on the shore?

b) If the river is 325 m wide, how far downstream has the boat moved by the time it reaches the north shore?

See Sample Problem 3F

53. A hunter wishes to cross a river that is 1.5 km wide and that flows with a speed of 5 km/hr. The hunter uses a small powerboat that moves at a maximum speed of 12 km/hr with respect to the water. What is the minimum time needed for crossing?

See Sample Problem 3F

**** Honors:

In problem 53, what is the hunter’s displacement? Suppose someone is .2 downstream from the hunter’s original position and starts 3 minutes after him. What speed and bearing would they have to have to catch him on the bank?