# 2 point masses each having mass #m# are placed at a distance #2a#.Escape velocity for a mass #m# projected from position P?

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all the three masses lie in the same straight line and the point P is the midpoint of the distance separating the 2 masses,i.e,P is situated at a distance #a# from each of the masses #m# .

all the three masses lie in the same straight line and the point P is the midpoint of the distance separating the 2 masses,i.e,P is situated at a distance

If all three bodies are free to move, then this is a special case of the three body problem, where predicting the final outcome is extremely difficult.

If this mass can escape, i.e. reach an infinitely distant point, its final potential energy is

Conservation of energy tells us that

Thus

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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