Relative_Motionx 105.2 KB

filercaliforniaMechanics

Nov 14, 2013 (3 years and 1 month ago)

155 views

You’ve probably heard the saying
“motion is relative.” Or perhaps you’ve
heard people speak about Einstein’s
Theory of Relativity and Einstein’s
Theory of Special Relativity. But what is
this relativity concept?

You should have said that the backpack is not
moving, it’s just lying there. Because you are
the observer and you are traveling at the same
speed as the bus.


If you are riding on the bus and you put your
backpack down on the seat beside you, how
fast is the backpack moving?

Well you should have said it depends
on how fast the bus is moving.

Using Vectors to describe motion





Consider a plane traveling with a velocity of 100 km/hr,
South that encounters a
side wind

of 25 km/hr, West.
What would the resulting velocity of the plane be?

Pythagorean Theorem


(100 km/hr)
2

+ (25 km/hr)
2

= R
2

10,000 km
2
/hr
2

+ 625
km
2
/hr
2

= R
2


10,625 km
2
/hr
2

= R
2



(10,625 km
2
/hr
2
) = R


103.1 km/hr = R


Lets find the angle


tan (
ᶿ
) = (opposite/adjacent)


tan (
ᶿ
) = (25/100)


theta = tan
-
1

(25/100)


theta = 14.0 degrees


Question:
A train travels at 60 m/s to the east with
respect to the ground. A businessman on the train
runs at 5 m/s to the west with respect to the train. Find
the velocity of the man with respect to the ground.

First determine what information you are given.
Calling east the positive direction, you know the
velocity of the train with respect to the ground
(
v
TG
=60 m/s). You also know the velocity of the
man with respect to the train (
v
MT
=
-
5 m/s).
Putting these together, you can find the velocity of
the man with respect to the ground.

60m/
s

-
5m/s

+


A bird flies directly into a wind. If the bird’s
forward speed relative to the wind is 58.0
km/h and the wind’s speed in the opposite
direction is 55.0 km/h, relative to Earth,
how long will it take the bird to fly 1.4 km?