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Gennadij [26K]
3 years ago
10

A 100 kg bungee jumper leaps from a bridge. The bungee cord has an un-streched equilibrium length of 10 m, and a spring constant

of 35 N/m. What is the greatest vertical distance below the bridge surface that the bungee jumper will reach? Enter your answer as a positive number in meters, but do not enter units.
Physics
2 answers:
nika2105 [10]3 years ago
6 0

Answer:

11.78meters

Explanation:

Given data

Mass m = 100kg

Length of cord= 10m

Spring constant k= 35N/m

At the greatest vertical distance, the spring potential energy is equal to the gravitational potential energy

That is

Us=Ug

Us= 1/2kx^2

Ug= mgh

1/2kx^2= mgh

0.5*35*10^2= 100*9.81*h

0.5*35*100=981h

1750=981h

h= 1750/981

h= 1.78

Hence the bungee jumper will reach 1.78+10= 11.78meters below the surface of the bridge

Alika [10]3 years ago
6 0

Answer:

X=74.7

Explanation:

From the question we are told that:

Mass m=100kg

Length l=10m

Spring constant \mu=35N/m

Generally the equation for potential energy of mass is mathematically given by

 P.E_m=mgh

Since

 P.E_m=P.E_s

Where

 P.E_s =potential energy of spring

Therefore

m*g*(x+10) = 0.5*k*\mu^2

100*9.8*(x+10) = 0.5*35*\mu^2

980*(x+10) = 17.5*\mu^2

980*x+9800 = 17.5*\mu^2

 17.5*\mu^2 - 980*\mu - 9800 = 0

Comparing the equation above with standard quadratic equation

 17.5*\mu^2 - 980*\mu - 9800 = 0

 ax^2+bx+c=0

Giving

  a=17.5\\  b=-980\\  c=-9800

Solving Quadratic equation the roots of the equation is given as

 \mu_1=64.66

 \mu_2=-8.661

Since

\mu can not be -ve

Therefore

The vertical distance attained by the bungee jumper is given as

 X=\mu+l

 X=64.7+10

 X=74.7

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