Everything Science Grade 12

CHAPTER 6. MOTIONIN TWO DIMENSIONS 6.5

boat to be 5 m·s−^1 due East. Both perspectives are correct as long

as the frame of the observer is considered.

Example 14: Relative Velocity 2

QUESTION

It takes a man 10 s to ride down an escalator. The same man takes 15 s towalk

back up the escalator against its motion. How long will the man take towalk

down the escalator at the same rate he was walking before?

SOLUTION

Step 1 : Identify what is required and what is given

We are required to determine the time taken for a man to walk

down an escalator, withits motion. We are given the time taken

for the man to ride down the escalator and thetime taken for the

man to walk up it, against its motion.

Step 2 : Determine how to approach the problem

Select down as positiveand assume that the escalator moves at a

velocity ve. If the distance of the escalator is xethen:

ve=

xe

10 s

(6.7)

Now, assume that the man walks at a velocity vm. Then:

ve− vm=

xe

15 s

(6.8)

We are required to find t in:

ve+ vm=

xe

t

(6.9)

Step 3 : Solve the problem

We find that we have three equations and threeunknowns (ve,

vmand t). Add (6.8) to (6.9) to get:

2 ve=

xe

15 s

+

xe

t

Substitute from (6.7) to get:

2

xe

10 s

=

xe

15 s

+

xe

t