Answer:
a ) 2.68 m / s
b ) 1.47 m
Explanation:
The jumper will go down with acceleration as long as net force on it becomes zero . Net force of (mg - kx ) will act on it where kx is the restoring force acting in upward direction.
At the time of equilibrium
mg - kx = 0
x = mg / k
= (60 x 9.8 ) / 800
= 0.735 m
At this moment , let its velocity be equal to V
Applying conservation of energy
kinetic energy of jumper + elastic energy of cord = loss of potential energy of the jumper
1/2 m V² + 1/2 k x² = mg x
.5 x 60 x V² + .5 x 800 x .735 x .735 = 60 x 9.8 x .735
30 V² + 216.09 = 432.18
V = 2.68 m / s
b ) At lowest point , kinetic energy is zero and loss of potential energy will be equal to stored elastic energy.
1/2 k x² = mgx
x = 2 m g / k
= (2 x 60 x 9.8) / 800
= 1.47 m
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Answer:

Explanation:
The gravitational potential energy of an object is defined as:

where
m is the mass of the object
g is the gravitational acceleration
h is the height of the object above a reference level (usually, the ground)
For the boulder in the problem,
m = 1000 kg
g = 10 N/kg
h = 6 m
Substituting,

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