Question

Part 1: Vertical jumps (7 pts)

Have a subject stand as close as possible to the wall with arms extended as high as possible next to the tape measure attached to the wall. Note the height the subject is able to reach while standing. Have the subject perform a maximal vertical jump while another team member records the time it takes for the subject to do the entire vertical jump (from the moment he leaves the ground until he touches the ground again). Note the max height s/he reaches. Calculate the vertical displacement by subtracting the difference between the height reached for the jump and the height reached while standing. Repeat this procedure for a second subject. Calculate the mechanical work produced by the person to reach the height, the potential energy of the person at his/her apex, the kinetic energy of the person immediately prior to the take-off, and the kinetic energy at his/her apex for two subjects.

Work, Energy, Power Charts

***Show work in space provided below charts. Be sure to include appropriate units.***

1. Vertical Jumps (g = 9.81 m/s²)

Performer	1	2	3
Mass	77.4 kg	53.6 kg	125 kg
Weight
Vertical displacement	55.88 cm	48.26 cm	142.24 cm
Total time	1.04s	.92s	2.34 s
Flight time
Average velocity
Potential energy at apex
Kinetic energy at takeoff
Kinetic energy at apex
Caloric energy (convert from Joules to Calories) [1 Calorie = 4187 J]

Answer 1

Performer 1

mass, m = 77.4 kg

Weight, W = mg = 77.4*9.81 kg = 759.29N

Vertical displacement, h = 55.88 cm = 0.5588 m

Total time, T = 1.04 s

Flight time, t = 1.04/2 = 0.52 s

Average velocity, V = h/t = 55.88/0.52 cm/s = 107.46 cm/s = 1.07 m/s

Potential energy at the apex, U = mgh = 77.4*9.81*0.5588 J=424.29 J

Kintetic energy at take off, = Potential energy at the apex

Kinetic energy at apex,

Caloric energy,

Power,

Performer 2

mass, m = 53.6 kg

Weight, W = mg = 53.6*9.81 kg=525.82 N

Vertical displacement, h = 48.26 cm = 0.4826 m

Total time, T = 0.92 s

Flight time, t = 0.92/2 = 0.46 s

Average velocity, V = h/t = 48.26/0.46 cm/s = 104.9 cm/s = 1.049 m/s

Potential energy at the apex, U = mgh = 53.6*9.81*0.4826 J=253.76 J

Kintetic energy at take off, = Potential energy at the apex

Kinetic energy at apex,

Caloric energy,

Power,

Performer 3

mass, m = 125 kg

Weight, W = mg = 125*9.81 kg = 1226.25 N

Vertical displacement, h = 142.24 cm = 1.4224 m

Total time, T = 2.34 s

Flight time, t = 2.34/2 = 1.17 s

Average velocity, V = h/t = 142.24/1.17 cm/s = 121.6 cm/s = 1.216 m/s

Potential energy at the apex, U = mgh = 125*9.81*1.4224 J=1744.22 J

Kintetic energy at take off, = Potential energy at the apex

Kinetic energy at apex,

Caloric energy,

Power,

Performer	1	2	3
Mass	77.4 kg	53.6 kg	125 kg
Weight	759.29 N	525.82 N	1226.25 N
Vertical displacement	55.88 cm	48.26 cm	142.24 cm
Total time	1.04 s	0.92 s	2.34 s
Flight time	0.52 s	0.46 s	1.17 s
Average velocity	107.46 cm/s	104.9 cm/s	121.6 cm/s
Potential energy at apex	424.29 J	253.76 J	1744.22 J
Kinetic energy at takeoff	424.29 J	253.76 J	1744.22 J
Kinetic energy at apex	0	0	0
Caloric energy	101.34 cal	60.61 cal	416.6 cal
Power	815.9 W	551.6 W	1490.8 W