There is an 18 metre high crane for bungy jumping. On jumping you go up and down

Question

There is an 18 metre high crane for bungy jumping. On jumping you go up and down a number of times before reaching a stable position from where you can be brought back to the ground. The first rebound is 6 metres high and this distance gets smaller by 20% each time you bounce back.

Answer the following;

(a) Create an iterative model to represent the above information.

(b) Find the closed form solution of this model

(c) Calculate the number of times you will bounce back before the distance of the rebound falls below 50cm?

Explanation / Answer

a)

Each time the distance gets smaller by 20 percent

So, for 1st jump , the distance is 6m

for 2nd jump, it is 6*(1 - 20/100) = 0.8*6

for 3rd jump, it is 0.8*6*(1-20/100) = 0.8^2*6

So, fo nth jump, the height is : = 0.8^(n-1)*6

So, rebound height , h = 6*0.8^(n-1) <------answer

For h < 50 cm(or 0.5m),

Now, 0.5 = 6*0.8^(n-1)

So, n = 12.1

So, for the 13th rebound, the distance falls below 50 cm <--------answer

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