# A daredevil wishes to bungee-jump from a hot-air balloon 70.5 m above a carnival midway.?

He will use a piece of uniform elastic cord tied to a harness around his body to stop his fall at a point 15.0 m above the ground. Model his body as a particle and the cord as having negligible mass and a tension force described by Hooke's force law. In a preliminary test, hanging at rest from a 5.00-m length of the cord, the jumper finds that his body weight stretches it by 1.65 m.

He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon.

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(a) What length of cord should he use?

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(b) What maximum acceleration will he experience?

### 3 Answers

- WhomeLv 78 months agoFavorite Answer
Use work energy theory.

Assume the balloon is stationary during the event.

from the preliminary test, we can find the spring constant k by summing forces to zero.

kx - mg = 0

kx = mg

k = mg/x

k = mg/1.65

as this was a 5 meter cord when relaxed, we can determine a k' for a unit length of cord

k' = 5(mg/1.65)

The maximum distance of fall desired is

70.5 - 15.0 - 55.5 m

during the jump, the potential energy will convert to spring potential

PE = PS

mgh = ½kx²

if the initial length of cord is L

x = 55.5 - L

and our spring constant will be

k = k'/L

55.5mg = ½(k' / L)(55.5 - L)²

55.5mg = ½(3.03mg) / L)(55.5 - L)²

55.5 = ½(3.03) / L)(55.5 - L)²

36.63 = (1 / L)(55.5 - L)²

36.63L = 3,080.25 - 111L + L²

0 = 3,080.25 - 147.63L + L²

quadratic formula

L = (147.63 ±√(147.63² - 4(1)(3080.25))) / (2(1))

L = 25.148 m

or

L = 122.5 m which we ignore as it cannot function in this scenario.

L = 25.1 m ANSWER

With the length of cord set, the stretch will be

x = 55.5 - 25.1 = 30.4 m

The force applied by the cord at max stretch is

F = kx

F = (k'/25.1)(30.4)

F = (5(mg/1.65)/25.1)(30.4)

F = 3.67mg

so the maximum acceleration experienced by the jumper will be

a = F/m

a = 3.67 mg / m

a = 3.67 g's

while an observer on the ground will see the jumper's body appear to accelerate upward at one g less or

a = 2.67 g or about 26.2 m/s²

I hope this helps

Please select as Best Answer if it does.

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- audreyLv 78 months ago
Ok. Does he want to win a teddy bear? What's your question?

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- WhomeLv 78 months agoReport
Yahoo limits the title length, you may wax eloquent on the question area. Maybe you should look for that area. Updates make for a very chopped up question.

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