Two kids are trying to pick some apples that are on the other side of the fence

Question

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? I need to see the work, not just the solution. Thank you!

Explanation / Answer

here,

mass of kid 1 , m1 = 50 kg

mass of kid 2 , m2 = 40 kg

let the distance of the 40 kg mass

height of the fence , h = 1.5 m

taking moment of force about the fence

m1*g*h/tan(40) -m2*g*x**cos(40) = 0

50 * 9.8*1.5/tan(40) - 40*9.8*x*cos(40) = 0

x = 2.92 m

the height up the ladder the lighter kid goes , x' = x + h/sin(40)

x' = 2.92 + 1.5/sin(40)

x'= 4.93 m

the height up the ladder the lighter kid goes is 4.93 m

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