Everything Science Grade 11

CHAPTER 11. VECTORS 11.7

Next we simply add thetwo displacements to give the resultant:

�xR = (+10m) + (− 2 ,5m)

= (+7,5)m

Step 6 : Quote the resultant

Finally, in this case towards the wall is the positive direction, so: �xR= 7,5 m

towards the wall.

Example 6: Subtracting vectors algebraically I

QUESTION

Suppose that a tennis ball is thrown horizontally towards a wall at aninitial velocity of 3

m·s−^1 to the right. After striking the wall, the ball returns to the thrower at 2 m·s−^1. Determine

the change in velocity of the ball.

SOLUTION

Step 1 : Draw a sketch

A quick sketch will helpus understand the problem.

3 m·s−^1

2 m·s−^1

Wall

Start

Step 2 : Decide which methodto use to calculate the resultant

Remember that velocityis a vector. The change in the velocity of the ballis equal

to the difference between the ball’s initial and final velocities:

Δ�v = �vf− �vi

Since the ball moves along a straight line (i.e. left and right), we can usethe

algebraic technique of vector subtraction just discussed.

Step 3 : Choose a positive direction

Choose the positive direction to be towardsthe wall. This means that the nega-

tive direction is away from the wall.

Step 4 : Now define our vectors algebraically

�vi = +3m· s−^1

�vf =−2m· s−^1

Step 5 : Subtract the vectors

Thus, the change in velocity of the ball is: