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Lesson
NAME ______________________________________ DATE _______________ CLASS ____________________
Two-Dimensional Motion and Vectors
Problem F
RELATIVE VELOCITY
PROBLEM
The world’s fastest current is in Slingsby Channel, Canada, where the
speed of the water reaches 30
...
Suppose a motorboat crosses the
channel perpendicular to the bank at a speed of 18
...
Find the velocity of the motorboat relative to the water
...
0 km/h along the channel (velocity of the water, w,
with respect to the bank, b)
vmb = 18
...
DEFINE
vmw = ?
vwb
Diagram:
vmb
vmw
2
...
Use the Pythagorean theorem to calculate the magnitude of the resultant velocity,
and use the tangent function to find the direction
...
The tangent of the angle between vmb and vmw
is equal to the ratio of the magnitude of vwb to the magnitude of vmb
...
CALCULATE
Substitute the values into the equation(s) and solve: Choose the positive root
for vmw
...
0 + 30
...
0
h
h
h
Copyright © by Holt, Rinehart and Winston
...
vmw = vmb + vwb
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Lesson
NAME ______________________________________ DATE _______________ CLASS ____________________
The angle between vmb and vmw is as follows:
km
30
...
0° away from the
km =
q = tan−1
oncoming current
18
...
EVALUATE
The motorboat must move in a direction 59° with respect to vmb and against
the current, and with a speed of 35
...
0 km/h perpendicular to the bank
...
In 1933, a storm occurring in the Pacific Ocean moved with speeds
reaching a maximum of 126 km/h
...
If a gull flies east through the storm with a speed of 40
...
George V Coast in Antarctica is the windiest place on Earth
...
00 × 102 km/h
...
50 × 102 km/h relative to the wind, how long does it
take the plane to fly between two research stations that are 250 km apart?
Copyright © by Holt, Rinehart and Winston
...
3
...
0 m/s for the leatherback turtle
...
0 m/s relative to
the water
...
0 m/s and it moves at a right
angle to the turtle’s motion, what is the turtle’s displacement with respect
to the river’s bank after 1
...
California sea lions can swim as fast as 40
...
Suppose a sea lion begins to chase a fish at this speed when the fish is 60
...
The fish, of
course, does not wait, and swims away at a speed 16
...
How long
would it take the sea lion to catch the fish?
5
...
0 km/h
...
The geese pass each other
40
...
Calculate the initial distance between the geese
...
The fastest snake on Earth is the black mamba, which can move over a
short distance at 18
...
Suppose a mamba moves at this speed toward a rat sitting 12
...
The rat immediately begins to run away at
33
...
If the rat jumps into a hole just before the mamba can catch it, determine the length of time that the chase
lasts
...
vse = 126 km/h north
vgs = 40
...
0 km/h)2ෆෆ126 km/h)2
4
vge = ͙1
...
59 ×ෆ0ෆෆෆෆ/ෆ2
ෆෆ × 1ෆ kෆෆෆෆෆ 1ෆෆෆ 1ෆ k m2ෆෆ
h
vge = ͙1
...
4° north of east
vgs
40
...
vwe = −3
...
50 × 102 km/h
∆x = 250 km
3
...
0 m/s north
vwb = 3
...
0 min
vpe = vpw + vwe = 4
...
00 × 102 km/h = 1
...
7 h
vpe 1
...
0ෆ/s)2ෆෆ3
...
0ෆ2/s2
vtwෆෆ vwb2
(9ෆ mෆෆ + (ෆෆෆෆෆ
81 mෆෆ + 9ෆ mෆෆ
II
vtb = ෆ0 ×ෆ01ෆ2/s2
9
...
5 m/s
60 s
∆x = vtb∆t = (9
...
0 min) = 570 m
1 min
vw b
3
...
0 m/s
4
...
0 km/h forward
vfw = 16
...
All rights reserved
...
0 m
5
...
0 km/h
v2E = −90
...
0 s
vsf = vsw − vfw = 40
...
0 km/h = 24
...
0 m
∆t = = = 9
...
0 km/h)
3600 s 1 km
v12 = v1E − v2E
v12 = 90
...
0 km/h) = 1
...
80 × 102 km/h) (40
...
00 × 103 m = 2
...
00 km apart
6
...
0 km/h forward
Vre = 0
...
00 km/h forward
∆x = 12
...
0 km/h − 6
...
0 km/h
∆x
12
...
0 km/h)
1h
103 m
∆t = 3
...
3–9