Jump height difference in two different gravities

In summary, the problem involves a high-jumper with a mass of 72 kg jumping in two different locations with a difference in gravity of 0.01 m/s^2. The student has attempted to solve the problem using different equations and varying gravities, but has not been successful. The answer involves using kinematics or the conservation of energy to find the ratio of jump heights in the two locations, rather than a constant difference in heights.
  • #1
Dreaming
7
0

Homework Statement



Gravity varies in two different places by 0.01 m/s^2. The jumper has a mass of 72 kg. What is the difference in jump height in each location? I have a couple of height measurements, but I'm pretty sure they are irrelevant because I am looking for a difference (and the problem says the difference in the heights listed is not due to gravity).

Homework Equations



I tried using F(jump)-F(weight) = ma, where a = 2h/t^2 and F(weight) = mg.
I also tried using delta x = 0.5g*t^2

The Attempt at a Solution


For both equations, I enter in the different gravities into two equations and subtract the two equations. I used 9.8 and 9.81, though I suppose I could use any two numbers varying by 0.01.
In both attempts, I come up with a difference of 0.005, but the answer checker tells me that I am wrong.
 
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  • #2
The energy of the jump is the same.
 
  • #3
voko, I do not need energy. Energy is not involved in this particular problem. Just acceleration, force, mass.
 
  • #4
You can't solve this with force. It is not constant.
 
  • #5
Here is the exact wording:

Because of Mexico City's altitude the acceleration of gravity there is lower than that in
Tokyo by about 0.01 m=s2. Suppose a high-jumper has a mass of 72 kg.

(b) Assume that he is able to jump with the same initial vertical velocity in both locations, and that all other conditions are the same except for gravity. How much higher should he be able to jump in Mexico City?

Energy is at the end of this course, and I am only 1/3 of the way in! This IS supposed to be a difficult problem... Oh well!
 
  • #6
Okay, what have you covered in the course so far?
 
  • #7
Just Newton's first and second laws. F=ma, v=x/t, a=v/t, and some related equations.
 
  • #8
With "Assume that he is able to jump with the same initial vertical velocity in both locations, and that all other conditions are the same except for gravity" and a = v/t, can you figure out how long it takes in both locations to reach the top point in a jump? Then, given this time, can you compute the vertical distance?
 
  • #9
From kinematics or conservation of energy, you will find the jump height is related to initial speed by $$v^2=2gh$$ ... from there you can easily find a ratio of the heights reached in the two locations.

However, the difference in heights is not a constant ... "how much higher" seems best interpreted as the ratio ... it is not "I jumped so-many cm higher" but "I jumped so many times higher".
 

1. How does gravity affect jump height?

Gravity plays a crucial role in determining jump height. The stronger the gravitational pull, the lower the jump height will be.

2. Why does jump height differ in two different gravities?

The difference in jump height is due to the gravitational force acting on an object. In areas with stronger gravity, the object will experience a greater downward force, resulting in a lower jump height.

3. How can jump height be measured in different gravities?

Jump height can be measured using various methods, including timing how long it takes for an object to reach its maximum height, or using sensors to track the height of the jump.

4. Can different body types affect jump height in different gravities?

Yes, different body types can have an impact on jump height in different gravities. For example, a person with stronger leg muscles may be able to jump higher in a weaker gravity compared to someone with weaker leg muscles.

5. Is there a maximum jump height in different gravities?

The maximum jump height achievable in different gravities depends on various factors such as the strength and size of the individual, as well as the surface they are jumping from. In weaker gravities, the maximum jump height may be higher due to the lower gravitational force acting on the body.

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