Physics, 14.04.2020 16:53 brandon1748

The jumper has a mass of 50 kg, and the bridge's height above the river is 150 m. The rope has an unstretched length of 11 m and stretches a distance of 4 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

Answers: 2

Show answers

Answers

Answer from: julesR9814

The speed of jumper is 54.22 m/s and the spring constant of the rope is 9187.5 N/m.

Given data:

The mass of jumper is, m = 50 kg.

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

The length of unstretched rope is, L = 11 m.

The stretched length is, L' = 4 m.

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

$mgh=\dfrac{1}{2}(kL'^{2} )$

Here, k is the spring constant.

Solving as,

$mgh=\dfrac{1}{2}(kL'^{2} )\\\\50 \times 9.8 \times 150=\dfrac{1}{2}(k \times 4^{2} )\\k = 9187.5 \;\rm N/m$

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

$v^{2} = u^{2} +2gh\\\\v^{2} = 0^{2} +2 \times 9.8 \times 150\\\\v= \sqrt{2 \times 9.8 \times 150}\\\\v =54.22 \;\rm m/s$

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:

link

Answer from: blue5488

The maximum speed of the jumper is 54.2m/s

The spring constant of the rope is

K=9.19KN/m

Explanation:

Step one

According to hook's law the applied force F is proportional to the extension e provided the elasticity is maintained

Step two

Given that

mass= 50kg

Height of bridge h=150m

Extention e=4m

Step three

To determine the maximum speed of the jumper

Since he is going with gravity we assume g=9.81m/s²

And we apply the equation of motion

V²=U²+2gh

where u= initial velocity of the jumper =0

h=height of bridge

Step four

Substituting we have

V²=0²+2*9.81*150

V²=2943

V=√2943

V=54.2m/s

Step five

To solve for the spring constant

We have to equate to potential energy of the jumper to the energy stored in the spring

Potential energy of the jumper =mgh

Energy stored in the spring =1/2ke²

Hence mgh=1/2ke²

Making k subject of formula we have

K=2mgh/e²

Substituting our data into the expression we have

K=2*50*9.81*150/4²

K=147150/16

K=9196.9N/m

K=9.19KN/m

Answer from: Quest

explanation:

newton's third law, for every action there is an equal and opposite reaction.

Answer from: Quest

Your answer is 32 hope i

Another question on Physics

Physics, 21.06.2019 20:00

What are segments of dna that code for a particular trait. a combination of dna and proteins make up what

Answers: 1

Answer

Physics, 22.06.2019 05:30

What do you think car designers do if the damage caused by a crash test is too severe?

Answers: 1

Answer

Physics, 22.06.2019 12:50

Air is contained in a variable-load piston-cylinder device equipped with a paddle wheel. initially, air is at 400 kpa and 17°c. the paddle wheel is now turned by an external electric motor until 75 kj/kg of work has been transferred to air. during this process, heat is transferred to maintain a constant air temperature while allowing the gas volume to triple. calculate the required amount of heat transfer in kj/kg.

Answers: 2

Answer

Physics, 22.06.2019 13:50

Two students, each riding bicycles, start from the same apartment building and ride to the same building on campus, but each takes a different route. the first student rides 1100 m due east and then turns due north and travels another 1430 m before arriving at the destination. the second student heads due north for 1930 m and then turns and heads directly toward the destination.at the turning point, how far is the second student from the destination?

Answers: 3

Answer

You know the right answer?

The jumper has a mass of 50 kg, and the bridge's height above the river is 150 m. The rope has an un...

Questions