Impulse and change in velocity

TASK: The following task assumes that all of the elements of the support package have been undertaken and that students have attended the lecture on impulse.

The task requires you to compare the effectiveness of two take off techniques for the vertical jump by calculating the take off velocity. The basic premise is that the higher the take off velocity the higher the jumper will travel. Technique 1 involves the particpant in the experiment doing a counter movement in a downwards direction prior to immediately driving upwards - this is the same technique that is shown in the video associated with this project. The second technique does not involve the counter movement. The jumper starts in a squat position and then drives upwards. Two sets of data recording the vertical force are available in Table 1 and Table 2 for techniques 1 and 2 respectively. The particpants mass was 78.5kg. You will need to use the trapezium equation which is given as follows:

Table 1 Vertical Ground Reaction Force Data for 78.5kg participant during a counter movement take off for a vertical jump.

Frame (0.02s)	Force (N)
1	769
2	756
3	708
4	666
5	590
6	539
7	541
8	561
9	593
10	625
11	678
12	690
13	744
14	876
15	1193
16	1562
17	1752
18	1728
19	1679
20	1662
21	1638
22	1315
23	0

 

Table 2 Vertical Ground Reaction Force Data for 78.5kg participant during a take off for a vertical jump without a counter movement.

Frame (0.04s)	Force (N)
1	769
2	783
3	786
4	808
5	861
6	942
7	1013
8	1062
9	1076
10	1115
11	1220
12	1396
13	1530
14	1625
15	1691
16	1743
17	1716
18	1560
19	1298
20	886
21	190
22	0

The suggested approach to undertaking the calculations is as follows:

• remember that you are doing two separate calculations and inspection of the data in the talble will show that different sampling rates have been used - this is important to note for the application of the trapezium rule.
• first calculate the ground reaction impulse by applying the trapezium rule to the data in Table 1. Log your result.
• next calculate the gravitational impulse. You will need to work out the jumper's weight (assume acceleration due to gravity is 9.81ms^-2). As the gravitational force does not vary you will not need to use the trapezium rule - a simple area calculation of a rectange is all that is required (look back at the Impulse section of the project if you need to revise this idea).
• calculate the net impulse by taking the gravitational impule away from the ground reaction force impulse.
• lastly divide the net impulse by the subjects mass and you should now have the change in velocity value you require for the first jump.Remember that as the jumpe started from a zero velocity the change you have calcualted is the actual take off velocity.
• repeat the procedure for technique 2 and compare your results.

TASK: Post your results to the Blackboard discussion area and see if you can arrive at a consensus as to which of the two techniques will produce the heighest take off velocity for this particular jumper on this occasion.