P20 Unit A Review pt B: Vectors
Adding Colinear Vectors
- Vectors that are colinear (in the same dimension) can be added directly.
ex) Ashley gets on a train at a train station. The train moves to a position 350 km [W] of the
station, then turns around and moves to a position 160 km [E] of the station. Find the
displacement of the train.
Adding Non-colinear Vectors
- To add vectors at right angles, use trig.
- Called "finding the resultant"
ex) A boat is crossing a river with a current of 7.0 m/s [N]. The boat has a water speed of 12 m/s
[W]. Determine the speed of the boat from the point of reference of an observer on the shore.
ex) LD is crossing the river Spruce Grove in his homemade bathtub boat. He rows, rows, rows
his boat due north at 4.00 m/s. The river flows gently at 6.00 m/s due east and is 360 m across.
Determine the direction, relative to the shore, that LD will move.
ex) Future LD is skiing the 2010 Birkebeiner at Elk Island Park. He skis for 21 km at [220°] and
19 km at [335°]. The magnitude of his resultant displacement is ___________ km.
Hint: You can only add vectors that are colinear.
ex) A canoe is paddling across a stream which is 25 m wide. The stream has a current of 3.2 m/s
East. If the canoe paddles directly North with a velocity of 4.0 m/s, how far downstream will it
end up?
ex) A canoe is paddling across a stream which is 25 m wide. The stream has a current of 3.2 m/s
East. If the canoe paddles directly North with a velocity of 4.0 m/s, how far downstream will it
end up?
Draw two diagrams, one for velocity and one for displacement. The angle is the same in both
diagrams.
ex) Augustous Gloop wants to swim across a river of chocolate to a point directly North across
from his starting point.
a) If Augustous can swim at 20 m/s and the river has a current of 1.5 m/s West, what direction
must he start off at?
b) If the river is 6.75 m wide, how long will it take until Augustous crosses the river?
ex) An object is thrown horizontally with a velocity of 10.0 m/s from the top of a 90.0 m
building. How far from the base of the building will the object land and what will its final
velocity be?
- How long the object is in the air:
- How far the object lands from the cliff:
ex) A watermelon is thrown from the top of a very tall watermelon tree with a horizontal velocity
of 18.0 m/s. If the melon hits the ground 100 m from the tree, how high is the tree?
ex) I throw an old M.C. Hammer tape at an angle of 20o N of E with a velocity of 15 m/s. How
long is the tape in the air?
- How long is the projectile in the air, given vi?
ex) LD shoots a 3-ball from half-court. The ball reaches a height 20 m from its release point.
How long was the ball in the air?
- How long was the object in the air, given dy?
- How high does it go?
- How far does it go (range)?
ex) LD's potato gun fires with a velocity of 5.00 m/s [60o].
a) How long is the potato in the air?
b) How high does the potato go?
c) What is the potato's range?
ex) LD and Jake are playing hockey against each other. The score is 3-2 and LD’s team is
winning because they have LD. Jake team has pulled their goalie. Oooh, the suspense!
LD shoots the puck from his zone directly towards the open net at an angle of 30° to the
horizontal with a velocity of 20 m/s (the perfect shot to land exactly in the empty net). Jake,
starting from 5.0 m directly ahead of LD, chases after the puck with a constant velocity of 9.75
m/s the instant after the puck is fired.
Will Jake be able to reach the puck before it hits the ice and goes in the net?
Thus Ends Unit A
- Please Review:
- Your Notes
- Your 3 Unit Assignments
- Your 2 Quizzes
- Your Unit A Exam (after school or at lunch with LD)
- More Unit A Review Questions on: Pg 118-121