Different initial vertical velocities on different planets

[gbean]

Homework Statement

Suppose that I am jumping on the Earth, and I weigh 130 lbs. I push off with an initial vertical velocity of 2 m/s, and reach my highest height at 4 m.

If I were to jump on a different planet with an extra 130 lbs (earth weight) because of a space suit etc., would I have a different vertical velocity?

Homework Equations

delta y = vyi(t) + a(t^2)
vyi = initial vertical velocity
delta y = height
Earth has gravity acceleration constant = 9.8 m/s^2

The Attempt at a Solution

If I were on a planet with a gravity acceleration constant greater than Earth, I would think that I would have a smaller initial vertical velocity because I have to overcome a greater force of gravity.

On the other hand, if I were on a planet with a gravity acceleration constant less than Earth, I would think I would have a greater initial vertical velocity because I have to overcome less force of gravity.

Apparently the initial vertical velocities (neglecting the extra mass of the space suit) are all the same on all planets. I don't understand this! Does this also mean that since they are all the same, if I add the constraint that I have extra mass, I will have a smaller initial vertical velocity (even if I am on a planet with weaker gravity)??

 

[PeterO]

Homework Statement

Suppose that I am jumping on the Earth, and I weigh 130 lbs. I push off with an initial vertical velocity of 2 m/s, and reach my highest height at 4 m.

If I were to jump on a different planet with an extra 130 lbs (earth weight) because of a space suit etc., would I have a different vertical velocity?

Homework Equations

delta y = vyi(t) + a(t^2)
vyi = initial vertical velocity
delta y = height
Earth has gravity acceleration constant = 9.8 m/s^2

The Attempt at a Solution

If I were on a planet with a gravity acceleration constant greater than Earth, I would think that I would have a smaller initial vertical velocity because I have to overcome a greater force of gravity.

On the other hand, if I were on a planet with a gravity acceleration constant less than Earth, I would think I would have a greater initial vertical velocity because I have to overcome less force of gravity.

Apparently the initial vertical velocities (neglecting the extra mass of the space suit) are all the same on all planets. I don't understand this! Does this also mean that since they are all the same, if I add the constraint that I have extra mass, I will have a smaller initial vertical velocity (even if I am on a planet with weaker gravity)??

Firstly - if you jump with an initial velocity of 2 m/s on Earth, you won't reach a maximum height of 4 metres - in fact you won't even make it to 1 metre.

Secondly, the velocity with which you leave the ground can become a function of how quickly you can activate your leg muscles.
It might seem that if you were only one tenth your mass, you may be able to achieve 10 times the speed, but consider this: If you lie on your back, with your legs curled, and then as quickly as possible, straighten your legs - can you achieve a speed of 20 m/s [72 km/h] with your feet? Probably not. Probably faster than 2 m/s but not 20 m/s. [I am assuming that onlt about 10% of your weight is in your legs]

Perhaps your problem has be phrased to say you have a common "launch velocity" for simplicity.