answer this physics question?

Question

a wedge wtih mass M rests on a frictionless table top. a block of mass m is placed on the wedge, and a horizontal force F is applied to the wedge. what is the magnitude of F if the block is to remain at a constant height above the table top.

i need the step-by-step solutions!
answer: F= (M+m) gtan(theta)

Answer 1

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Answer 2

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Answer 3

you know that F=ma

m = the mass of the system = masll of block + mass of wedge = M+M

now, F=(M+m)a

you want to maintain a constant height, so you are only concerned about acceleration in the y direction, which is gravity, or g

the wedge helps you fight gravity and the amount of help you get is determined by theta, which is the angle of the wedge. you want to get the component of gravity which is fighting the constant height, which is g*tan(theta)

now, F=(M+m)*g*tan(theta)