contestada

It's your birthday, and to celebrate you're going to make your first bungee jump. You stand on a bridge 100 m above a raging river and attach a 30-m-long bungee cord to your harness. A bungee cord, for practical purposes, is just a long spring, and this cord has a spring constant of 40 N/m . Assume that your mass is 80 kg . After a long hesitation, you dive off the bridge. [Take g

Respuesta :

Answer:

The distance is 15.21 m.

Explanation:

Given that,

Height of bridge h= 100 m

Length = 30 m

Spring constant = 40 N/m

Mass = 80 kg

Suppose we need to find the distance when the cord reaches its maximum elongation

We need to calculate the distance

[tex]D= h+x[/tex]

[tex]D=100+x[/tex]

We need to calculate the gravitational potential energy

Using formula of gravitational potential energy

[tex]P.E_{i}=mgh[/tex]

Put the value into the formula

[tex]P.E=80\times9.8\times h[/tex]

[tex]P.E=784h[/tex]....(I)

We need to calculate the elastic energy in cord

Using formula of elastic energy in cord

[tex]E=\dfrac{1}{2}kx^2[/tex]

[tex]E=\dfrac{1}{2}\times40\times x^2[/tex]

[tex]E=20x^2[/tex].....(II)

We need to calculate the value of x

From equation (I) and (II)

[tex]784h=20x^2[/tex]

Put the value of h into the formula

[tex]784(100+x)=20x^2[/tex]

[tex]20x^2-784x-78400=0[/tex]

[tex]x=85.21\ m[/tex]

Cord will be extended by 85.21 m when jumper at maximum elongation of  the cord.

We need to calculate the distance

[tex]D=100-(30+85.21)[/tex]

[tex]D=-15.21\ m[/tex]

Negative sign shows the distance of under water.

Hence, The distance is 15.21 m.

Otras preguntas