Question

A bungee jumping platform is located 150m above ground and certified for people up to 110kg. The unstretched bungee rope is 40m long.

a) Calculate the speed of a bungee jumper after 40m free fall and calculate the time for this free fall!

b) After free fall the rope’s elasticity decelerates the bungee jumper. Every bungee jumper should stop at least 20m above ground. Calculate the spring constant such that a bungee jumper with mass 110kg will stop 20m above ground! Remark: Use a coordinate system which has y=0m at the ground and points upwards and use energy conservation.

Answer 1

Given data in diagram :

a).  Now the time required for this free fall can be calculated using kinematic equation:

Where S is the distance traveled ( 40 m in this case)

u is the initial velocity ( zero in this case)

t is the time taken to cover the S distance

a is the acceleration ( here a=g=9.8 m/s²)

Substituting the values we get:

or

Which is the time taken for the free fall of 40 m

Now to calculate speed of bungee jumper after 40m free fall we will use following kinematic equation:

Where v is the final velocity

u is the initial velocity ( zero in this case)

a is the acceleration (g in this case)

t is the time (2.86 seconds in this case)

Substituting the values we get:

Which is the required speed of the body after free fall of 40 m

b). Now as every bungee jumper should stop 20 m above ground. Therefore at 20 m height above the ground the Potential energy due to gravity will be equal to elastic potential energy of rope (Energy conservation ).

Where m is the mass of the body (110 kg in this case)

g is the acceleration due to gravity (9.8 m/s²)

h is the height above the ground( 20 m in this case)

k is the spring constant

x is the amount of stretched length ( 90 m in this case(see diagram))

Substituting the values we get:

Which is the required answer.

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