With what minimum speed must Jane begin her swing in order to just make it to Charlie

In summary, the minimum speed for Jane's swing can be calculated using a formula that takes into account the acceleration due to gravity, the length of the swing, and the angle of the swing at the lowest point. This minimum speed is significant because it is the lowest speed that Jane needs to reach Charlie on the other side. The length of the swing affects the minimum speed, with longer swings requiring a higher speed. If Jane's speed is higher than the minimum required, she will be able to swing back and forth multiple times. The minimum speed is not the same for every swing, as it depends on the length and starting angle of the swing.
  • #1
alevis
17
0

Homework Statement


Vernie, whose mass is 45.0 kg, needs to swing across a river filled with crocodiles in order to rescue Charlie,whose mass is 75.0 kg. However, she must swing into a constant horizontal wind force on a vine that is
initially at an angle of θ with the vertical. The width of the river between them is D = 60.0 m, F = 120 N, Length of

the rope L = 45.0 m, and θ = 60.0°.
(a) With what minimum speed must Jane begin her swing in order to just make it to the other side?
(b) Once the rescue is complete, Vernie and Charlie must swing back across the river. With what minimum

speed must they begin their swing?



Homework Equations


L=L-(Lcosθ)
KE = 1/2mv2
PE = mgh.


The Attempt at a Solution


PE = KE
mgh = 1/2mv2
 
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  • #3

gh = 1/2v2
v = √2gh
v = √(2*9.8*45*sin60)
v = 27.8 m/s

(a) To just make it to the other side, Jane must have a minimum speed of 27.8 m/s.

(b) To swing back across the river, Vernie and Charlie must have a minimum speed of 27.8 m/s as well. This is because the conservation of energy principle states that the total energy of a system remains constant. Since the initial energy of the system was used to cross the river, the same amount of energy is required to swing back across. Therefore, the minimum speed required remains the same.
 

1. How do you calculate the minimum speed for Jane's swing?

The minimum speed for Jane's swing can be calculated using the formula: v = √(gL(1-cosθ)), where g is the acceleration due to gravity, L is the length of the swing, and θ is the angle of the swing at the lowest point.

2. What is the significance of the minimum speed in Jane's swing?

The minimum speed is the lowest speed that Jane needs to achieve in order to successfully make it to Charlie on the other side. If her speed is lower than this, she will not have enough momentum to complete the swing and reach Charlie.

3. How does the length of the swing affect the minimum speed?

The longer the swing, the higher the minimum speed required for Jane to reach Charlie. This is because a longer swing means Jane will have to travel a greater distance, requiring more speed to overcome the force of gravity and reach the other side.

4. What happens if Jane's speed is higher than the minimum required?

If Jane's speed is higher than the minimum required, she will have enough momentum to not only reach Charlie, but also swing back and forth multiple times. This is because her initial speed provides her with enough energy to overcome the force of gravity and continue swinging.

5. Is the minimum speed the same for every swing?

No, the minimum speed will vary depending on the length of the swing and the angle at which Jane starts swinging. A longer swing or a higher starting angle will require a higher minimum speed for Jane to successfully reach Charlie.

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