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The jumper has a mass of 55 kg, and the bridge's height above the river is 150 m. The rope has an unstretched length of 8 m and stretches a distance of 5 m before bringing the jumper to a stop. Determine the maximum speed of the jumper and the spring constant of the rope. In your calculation, use g 10 N/kg. m/s Vmax k = N/m E.
Now suppose the jumper has a mass of 80 kg. Do you think the maximum speed of the jumper will increase, decrease, or stay the same? Will the rope need a larger, smaller, or the same spring constant to bring the jumper to a stop in the same distance as part D?

Sagot :

Answer:

The speed of jumper is 54.22 m/s and spring constant of the rope is 6468N/m.

Given data:

The mass of jumper is, m = 55 kg.

The height of bridge above the river is, h = 150 m.

The length of unstretched rope is, L = 8m.

The stretched length is, L' = 5m.

In this problem, when the jumper will jump then the potential energy of jumper will get converted into the spring potential energy of the rope. Then the relation will be,

potential energy of jumper  = spring potential energy of rope

Here, k is the spring constant.

Solving as,

mgh = 1/2 Kl^2

55 × 90.8 ×150 = 1/2 × k × 5 × 5

k=6468 N/m

Now, apply the third kinematic equation of motion to calculate the final speed of jumper as,

v^2 = U^2 + 2as

We get U= 54.22 m/s.

Thus, we can conclude that the speed of jumper is 54.22 m/s and the spring constant of the rope is 9187.5 N/m.

Learn more about the spring constant here: brainly.com/question/14670501.

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