Students picking apples, 40* ladder on fence

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Two kids are attempting to pick apples over a 1.5m high fence using a ladder positioned at a 40° angle. The problem involves calculating how far the lighter kid, weighing 40 kg, can climb the ladder before it tips over, while the heavier kid, weighing 50 kg, stands at the bottom. The equilibrium condition is based on balancing the torques, using the equation Mass1Radius1 = Mass2Radius2. A proposed solution of 2.91 meters was noted, but it does not match the provided options. The correct approach involves adding the distance to the pivot point to the calculated distance along the ladder.
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Homework Statement


Two kids are trying to pick some apples that are on the other side of the fence which is 1.5m high. Since there is a vicious dog on the other side, they decided to use a ladder and lean it against the fence. The ladder of negligible mass is placed at an angle of 40° to the horizontal. One kid of mass 50 kg stands at the bottom of the ladder while another kid of mass 40 kg goes up the ladder. How far up along the ladder can the lighter kid go before it tips over?

Homework Equations


dont know if this is correct. Mass1Radius1=Mass2Radius2 could not find examples in my textbook that are similar

The Attempt at a Solution


the answer i got was 2.91 meters but its not an option.
The book says for a system like this to be equilibrium that equation must be true. not sure how to approach this problem.
 
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clos561 said:

Homework Statement


Two kids are trying to pick some apples that are on the other side of the fence which is 1.5m high. Since there is a vicious dog on the other side, they decided to use a ladder and lean it against the fence. The ladder of negligible mass is placed at an angle of 40° to the horizontal. One kid of mass 50 kg stands at the bottom of the ladder while another kid of mass 40 kg goes up the ladder. How far up along the ladder can the lighter kid go before it tips over?

Homework Equations


dont know if this is correct. Mass1Radius1=Mass2Radius2 could not find examples in my textbook that are similar

The Attempt at a Solution


the answer i got was 2.91 meters but its not an option.
The book says for a system like this to be equilibrium that equation must be true. not sure how to approach this problem.
It would be nice if you showed your work. It seems you did this:
\frac{1.5}{sin(\frac{40}{180}\pi)}\frac{50}{40} = 2.92

Is that what you did? Were you balancing the torque about the point in contact with the fence?
 
yes that is what i did.
 
clos561 said:
yes that is what i did.

The distance up the ladder is equal to that quantity plus the distance to the pivot. Add 1.5/sin(40 degrees) to your answer.
 
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