Finding the height of a body through conservation of energy

[MichaelDunlevy]

Homework Statement

A 105 kg acrobat jumps up off a platform at a velocity of 2.50 m/s and lands on a teeter-totter 3.00 m below, where another acrobat is waiting. If the waiting acrobat has a mass of 62.5 kg, how high does she get?

Homework Equations

KE=(1/2)mv^2

PEg= mgh

The Attempt at a Solution

I calculated the PE of the first jumper (I disregarded the 2.50 m/s, it seemed unnecessary, please correct me if this is wrong), and got 3090 J.
I then plugged that into another PE=mgh equation for the second person and got 5.04 m. Is this correct?

 

[CompuChip]

The idea is correct, but you cannot just disregard the initial velocity of 2.5 m/s.
I am sure you agree that it matters whether he jumps upwards at 2.5 m/s, just drops himself off the platform, or dives down at 2.5 m/s.

Can you explain how the initial velocity affects the total energy of the first acrobat?

 

[MichaelDunlevy]

i can, but it would be different depending on the angle that he jumped 2.5 m/s. But, no matter what, the jumper's total energy will increase because of the jump. How can I apply it to this problem without a specific direction? I need to solve the answer soon.

 

[CompuChip]

Yeah, I guess you are right, so let's assume the 2.50 m/s was the vertical component. By how much with the total energy increase?

 

[MichaelDunlevy]

doesn't that depend on how long he is in the air?

 

[MichaelDunlevy]

Yeah, I guess you are right, so let's assume the 2.50 m/s was the vertical component. By how much with the total energy increase?

doesn't that depend on how long he is in the air?

 

[CompuChip]

No, that is the beauty of using energies rather than kinematic equations.

Assuming that no energy is lost (e.g. due to friction), the sum of all kinetic and potential energy at the time of the jump should be equal to the sum of all kinetic and potential energy at the time of landing ... or at any other time, for that matter.

You already used this in your original solution, but there you assumed that all energy at the start was in the form of potential energy, and it all gets converted to kinetic energy at the intermediate point where he meets the other acrobat. You need to review the first part of that assumption.