Everything Science Grade 12

6.5 CHAPTER 6. MOTIONIN TWO DIMENSIONS

on shore would observethe velocity of a boat tobe different than a passenger on the
boat.

Example 13: Relative Velocity

QUESTION

The speedometer of amotor boat reads 5 m·s−^1. The boat is movingEast

across a river which has a current travelling 3m·s−^1 North. What would the

velocity of the motor boat be according to an observer on the shore?

SOLUTION

Step 1 : First, draw a diagram showing the velocities involved.

3 m·s−^1

5 m·s−^1

Step 2 : Use the Theorem of Pythagoras to solve for theresultant of the

two velocities.

R =

�

(3)^2 + (5)^2

=

√

34

= 5,8 m· s−^1

tan θ =

5

3

θ = 59, 04 ◦

3 m·s−^1

5 m·s−^1

θ 5,8 m·s−^1

The observer on the shore sees the boat movingwith a velocity of

5,8 m·s−^1 at 59,04◦east of north due to thecurrent pushing the

boat perpendicular to its velocity. This is contrary to the perspec-

tive of a passenger on the boat who perceives the velocity of the