A 65.3-kg bungee jumper is standing on a tall platform (h0 = 48.9 m), as indicat

Question

A 65.3-kg bungee jumper is standing on a tall platform (h0 = 48.9 m), as indicated in the figure. The bungee cord has a natural length of L0 = 8.10 m and, when stretched, behaves like an ideal spring with a spring constant of k = 43.7 N/m. The jumper falls from rest, and it is assumed that the only forces acting on him are his weight and, for the latter part of the descent, the elastic force of the bungee cord. What is his speed when he is at the following heights above the water: (a) hA = 40.8 m, and (b) hB = 14.7 m?

Explanation / Answer

a. when the bungee jumper has height of ha=40.8, it means the distance between platform and him will be

L = h0 - ha = 48.9 - 40.8 = 8.1 m, which is a free fall.

so, speed at ha =40.8,

va = (2 g L)^(1/2)

= (2x9.81x8.1)^(1/2)

= 12.61 m/s.

b. Lb= 48.9 -14.7 = 34.2. L= 8.1 m of free fall, L' = 34.2 -8.1 =26.1 fall under influnece of bungee cord pull.

Using conservation of energy,

P.E. at the top = K.E. + spring energy at bottom

m g Lb = (1/2) m Vb^2 + 1/2 K L' ^2

vb^2= ((-K L'^2) + 2 m g Lb) / m

=[- 43.7 (26.1^2) + 2 x 65.3 x 9.81x 34.2]/65.3

= (-29768+43816)/65.3

= 13713/65.3 = 215

vb= 15.65 m/s

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