Calculating Maximum Height of a Child Swinging from a Rope

[kassy_in_the_sky]

Several children, pretending they are playing in the jungle, suspend a rope from an overhead tree limb. A child of mass 40 kg running at 8.0m/s grabs the rope and swings off the level ground.

a) What maximum height does the child reach?
b) How fast would a 30 kg child have to run to reach the same height as the 40 kg child?


½mv1²+mgh1 = ½mv2²+mgh2

a) m=40kg, v1=8.0m/s, h1=0m, g=9.8m/s², v2=0m/s (at max height v=0)

h2=?

½mv1²+mgh1 = ½mv2²+mgh2

½mv1²= mgh2

h2 = 3.27m = 3m (is this correct?)

im really confused with B... coz i got 8m/s... it doesn't make sense to me how they can run at the same speed and achieve the same height??!

this is really urgent... so please help me! >_< thanks!

 

[cookiemonster]

Notice that the mass drops out of the equations entirely. So the mass has no significance to the problem.

Intuitively, if you increase the mass, the person has greater kinetic energy when he starts. But getting to the same height also requires more energy. It works out that the increases in energy are identical.

cookiemonster

 

[kassy_in_the_sky]

thanks! ^^

 

[ablatter]

I believe that:

1. The initial inertial velocity is a convention between the different reference frames.

2. The total tensional energy of an isolated system is equal to zero.

3. The total energy of an isolated system is equal to zero.



Antonio A. Blatter

 

[ZapperZ]

Unfortunately, you're responding to a question that's about 4 years old.

Zz.

 

[RetardedBastard]

Unfortunately, you're responding to a question that's about 4 years old.

Zz.

Hmm, why is that frowned upon? I mean, physics problems are timeless afterall :)