A question with masses and distance to travel, find the time to travel so far

In summary, Jane needs to climb the vine at a speed where her weight is increased by a factor of 3.5 in order to reach Tarzan in a timely manner.
  • #1
maphco
24
0

Homework Statement


Jane wishes to quickly scale a slender vine to visit Tarzan in his treetop hut. The vine is known to safely support the combined weight of Tarzan, Jane, and Cheeta. Tarzan has twice the mass of Jane, who has twice the mass of Cheeta. If the vine is 60m long, what minimum time should Jane allow for the climb?


Homework Equations





The Attempt at a Solution


Mass of Tarzan = 2 * Mass of Jane = 4 * Mass of Cheeta
Mass of Jane = 2 * Mass of Cheeta
Mass of Cheeta = ?

Length of vine = 60m

Can you guys help me suck out any more relevant information, or assumptions, from this question that I've missed? I like to solve problems on my own, even if it takes me a month like one particular question.. I just want a heads up on what I'm missing.
 
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  • #2
I think the question is hinting at some use of Newton's second law...
 
  • #3
Is there a way that I can incorporate the Law of Conservation of Energy into this question?
 
  • #4
maphco said:
Is there a way that I can incorporate the Law of Conservation of Energy into this question?
I don't think so...
 
  • #5
maphco said:

Homework Statement


Jane wishes to quickly scale a slender vine to visit Tarzan in his treetop hut. The vine is known to safely support the combined weight of Tarzan, Jane, and Cheeta. Tarzan has twice the mass of Jane, who has twice the mass of Cheeta. If the vine is 60m long, what minimum time should Jane allow for the climb?

Homework Equations


The Attempt at a Solution


Mass of Tarzan = 2 * Mass of Jane = 4 * Mass of Cheeta
Mass of Jane = 2 * Mass of Cheeta
Mass of Cheeta = ?

Length of vine = 60m

Can you guys help me suck out any more relevant information, or assumptions, from this question that I've missed? I like to solve problems on my own, even if it takes me a month like one particular question.. I just want a heads up on what I'm missing.

the vine can support the weight of Jane + Tarzan = 2xJane + cheeta = 1/2xJane so the vine can support the weight of 3 and 1/2 Janes. So I think the question is asking how fast does jane have to climb so her weight is increased by a factor of 3.5. Alternatively, if jane is starting on the ground than she has to accelerate to move up the rope. The max force she can apply during the climb is 3.5 her weight where her weight is her mass at 1g or the rope breaks.
 
Last edited:
  • #6
F=ma?
 

1. What is the formula for calculating time to travel a certain distance with given masses and distance?

The formula for calculating time to travel is time = distance/velocity, where velocity is calculated by taking the square root of 2 x gravity x distance/mass.

2. Can the time to travel be affected by changes in mass or distance?

Yes, the time to travel will change if there are changes in the mass of the objects or the distance between them. As the mass increases, the force of gravity and the velocity will also increase, resulting in a shorter time to travel. Similarly, as the distance increases, the time to travel will also increase.

3. How is time to travel affected by different units of measurement?

The formula for calculating time to travel uses the standard units of meters for distance and kilograms for mass. If different units are used, the conversion must be made before plugging the values into the formula. For example, if the distance is given in kilometers, it must be converted to meters by multiplying by 1000.

4. What is the significance of mass and distance in the calculation of time to travel?

The mass and distance play a crucial role in determining the force of gravity and the velocity of the objects. The greater the mass, the greater the force of gravity, and the faster the objects will accelerate. Similarly, the greater the distance, the longer it will take for the objects to travel and reach each other.

5. Are there any other factors that can affect the time to travel?

Yes, there are other factors that can affect the time to travel, such as external forces like air resistance or friction. These forces can slow down the objects and increase the time it takes for them to reach each other. Other factors such as the shape and size of the objects or the medium they are traveling through can also have an impact on the time to travel.

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