Students picking apples, 40* ladder on fence

[clos561]

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.

 

[RoshanBBQ]

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?

 

[clos561]

yes that is what i did.

 

[RoshanBBQ]

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.