1
Lesson 1.5
Relative Velocity and Solving Problems in Projectile Motion
1
.
Relative Velocity:
All velocities are relative, it depends on the frame in which the measurement
is made. For example if you are in a car traveling in the positive x direction
at 20 m/s, a passenger sitting next to you will see you at rest while a person
standing by the side of the road will measure your velocity as 20 m.s
1
i. A
person in a car moving in the negative x direction at 15 m.s
1
will measure
your velocity as 35 m.s
1
i. Yet another person in a car traveling in the
positive x direction at 25 m/s will measure your velocity as –5 m.s
1
i!
In this section you will develop the skills needed to measure the velocity of
one object relative to another moving object. If two objects A and B are
moving, the velocity of A relative to B is obtained by the following two
steps.
(i)
Impose a velocity equal and opposite to that of B to both A and B.
This will bring B to rest and give A two velocities, its own and the
equal and opposite velocity of B imposed on it.
(ii)
Find the resultant of these two velocities of A. That will be the
velocity of A relative to B
To find the relative velocity of B with respect to A, bring A to rest by
applying an equal and opposite velocity of A to both and find the resultant
velocity of B.
Example 1
:
Car A has a velocity 10 m/s i and car B has a velocity 15 m/s i. Find (i) the
velocity of A relative to B and (ii) the velocity of B relative to A.
Solution:
(i)
Bring B to rest by imposing a velocity of –15 m.s
1
i to both A and B. A has
now two velocities 10 m.s
1
i and –15 m.s
1
i. The resultant of these two
velocities is given by 10 m.s
1
i – 15 m.s
1
i =
5 m.s
1
i
. The velocity of A
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relative to B is –5 m.s
1
. This means that for people in car B, car A will
appear to go backward with a velocity of 5 m.s
1
.
(ii)
Bring A to rest by imposing a velocity of –10 m.s
1
i to both A and B. B now
has two velocities 15 m.s
1
i and –10 m.s
1
i. The resultant of these two
velocities is given by 15 m.s
1
i – 10 m.s
1
i =
5 m.s
1
i
.
This means that for
people in car A, car B will appear to go forward at 5 m.s
1
.
Example 2
:
Car A has a velocity of –20 m.s
1
j and car B has a velocity of 15 m.s
1
j.
(i)What is the velocity of A relative to B? (ii) What is the velocity of B
relative to A?
Solution
:
(i)
To find the velocity of A relative to B, bring B to rest by applying a velocity
of –15 m.s
1
j to both A and B. A has now two velocities, 20 m.s
1
j and –15
m.s
1
j. The resultant of these two velocities is given by –20 m.s
1
j – 15 m.s
1
j =
35 m.s
1
j
.
(ii)
To find the velocity of B relative to A, bring A to rest by applying a velocity
of 20 m.s
1
j to both A and B. B has now two velocities 15 m.s
1
j and 20 m.s

1
j. The resultant of these two velocities is given by 15 m.s
1
j + 20 m.s
1
j =
35 m.s
1
j.
Example 3:
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 Fall '10
 George
 Physics, Projectile Motion, Velocity, vy, 30o

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