Everything Science Grade 12

6.3 CHAPTER 6. MOTIONIN TWO DIMENSIONS

Example 6: 2D Conservation of Momentum

QUESTION

In a rugby game, Player 1 is running with theball at 5 m·s−^1 straight down

the field parallel to theedge of the field. Player 2 runs at 6 m·s−^1 an angle

of 60 ◦to the edge of the fieldand tackles Player 1. In the tackle, Player 2

stops completely whilePlayer 1 bounces off Player 2. Calculate the velocity

(magnitude and direction) at which Player 1 bounces off Player 2. Both the

players have a mass of 90 kg.

SOLUTION

Step 1 : Identify what is required and what is given

The first step is to draw the picture to work out what the situation

is. Mark the initial velocities of both players in the picture.

60 ◦

v^1

=5 msi

−

1

v 2

i=8 ms

−

1

v 2 xi

2 v

yi

We also know that m 1 = m 2 = 90 kg and vf 2 = 0 ms−^1.

We need to find the final velocity and angle at which Player 1

bounces off Player 2.

Step 2 : Use conservation of momentum to solve the problem. First find

the initial total momentum:

Total initial momentum= Total final momentum. But we have

a two dimensional problem, and we need to break up the initial

momentum into x and y components.

pix = pfx

piy = pfy

For Player 1:

pix 1 = m 1 vi 1 x= 90× 0 = 0

piy 1 = m 1 vi 1 y= 90× 5