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Physics 2204
Worksheet 12: Relative Velocity in 2 - Dimensions
There are only two options for crossing a river (or flying a plane in a wind) that deal with right triangles. You can
either head straight across the current and get pushed downstream, or you can angle yourself into the current so as to
arrive straight across from where you started. The following example will look at both types of motion.
1.
In still water, Mr. Fifield can swim at 5.0 km/hr. If a river is flowing east at 3.0 km/hr.
a)
b)
If Mr. Fififeld heads straight across, what will be his velocity relative to the ground?
At what angle must Mr. Fifield point in order to arrive straight across the river?
Head straight across, get pushed downstream
Head into the current, end up straight across
1.
Draw diagram of the river with the current (it is easier to
put the current on the opposite side of the bank to where
you are)
1.
Draw diagram of the river with the current (it is easier to
put the current on the opposite side of the bank to where
you are)
2.
Draw the vector V om (your velocity in still water) as a
straight line across, be sure you connect tip to tail.
* notice the hypotenuse is our unknown
2.
Draw the vector V om (your velocity in still water) on an
angle, b e sure yo u connect tip to tail. * notice the
hypo tenuse is not our unknown
3.
Draw your resultant vector V og, it should be straight acro ss.
4.
Calculate the magn itude (size) of v og using Pythagora s
v om2
= v og 2 + v mg 2
2
5
= v og22 + 3 2
25
= v og + 9
16
= v og2
3.
4.
Draw your resultant vector V og, it should be at an angle.
Calculate the magn itude (size) of v og using Pythagoras
theorem.
v og2
= v om 2 + v mg 2
= 52 + 32
= 25 + 9
= 34
v og = 4.0 km/hr
5.
Calculate the angle using trig.
sin x
= opp
hyp
x
= sin -1 (3/5.8)
v og = 5.8 km/hr
5.
Calculate the angle using trig.
sin x
= opp
hyp
x
= sin -1 (3/5)
x = 37 /
x = 31 /
6.
6.
Write your resultant vector
Write your resultant vector
v og = 4.0 km/hr [N37W ]
v og = 5.8 km/hr [N31E]
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1.
Tarzan can swim at 2.0 m/s, the current is 1.0 m/s [E], and Tarzan is seen to swim directly across (assume
north). ANSWER 1.7 m/s [N]
2.
Tarzana can swim at 2.0 m/s, the current is 1.0 m/s [E], and Tarzana is seen to direct her body directly across
(north). ANSWER 2.2 m/s [N 27o E]
3.
Cheetah can also swim at 2.0 m/s. The water current is now 5.0 m/s [E]. Cheetah swims like Tarzana and points
directly north. ANSWER 5.4 m/s [N 68o E]
4.
For the case of a wind blowing from the east at 80 km/h and a plane capable of flying at 200 km/h, find
a) the velocity of the plane relative to the ground if the pilot points the plane north.
ANSWER 59.84 m/s [N21.8/E]
b) the velocity of the plane relative to the ground and the heading the pilot must take in order to fly directly
north. ANSWER 50.86 m/s [N23.6/W]
5.
A boat wishes to travel east. If there is a current of 10 km/h flowing north and the boat is capable of travelling at
30 km/h, find the heading and velocity of the boat as seen by a person on shore. Note: The term “heading” is
used to describe the direction the boat must point in order to successfully travel in its desired direction.
ANSWER 28 km/hr [E 20/S]
6.
A large cruise boat is moving at 15 km/h east relative to the water. A person jogging on the ship moves across
the ship in a northerly direction at 6 km/h. What is the velocity of
the jogger relative to the water? ANSWER 16 km/hr [E 22/N]
2
7.
An aircraft can fly at 275 km/hr in still air. The wind is blowing towards the east at 65 km/hr. If the aircraft flies
towards the north, calculate the resulting velocity of the aircraft relative to the ground. Your answer should
include a vector diagram.
[2]
8.
An aircraft can fly at 355 km/h with respect to the air. The wind is blowing towards the west at 95.0 km/h with
respect to the ground. The pilot wants to land at an airport that is directly north of his present location. Calculate
the direction in which the plane should head and its speed with respect to the ground. Include a vector diagram
in your answer.
[2]
9.
A river flows at 2.5 m/s [S]. A boater heads 3.5 m/s [E]. Calculate the boater’s resultant velocity with respect to
the shore. Include a labelled vector diagram in your answer.
[2]
3
10.
plane can travel at 350 km/h in still air and a wind is blowing at 65 km/h [S]. In what direction should the pilot
head in order to end up directly East of the starting point? Include a vector diagram in your answer.
[2]
11.
A boat heads directly North across a river with a current of3.5 m/s [E]. The boat can travel 5.5 m/s in still water.
What is the velocity of the boat relative to the Earth? Include a labelled vector diagram in your answer.
[2]
4