We can see that you posted your question twice, and left out different parts each time.
Fortunately, our crack WA cryptographic team was able to piece them together, and
we now believe that we know what you're trying to ask.
If we're correct, you have a vector of 100 units, pointing at an angle of 45 degrees ...
up and to the right, exactly between the positive 'x' and 'y' axes.
-- The horizontal component is 100 cos(45) = 100 x 1/2 sqrt(2) = 50 sqrt(2) = 70.711 (rounded)
-- The vertical component is 100 sin(45) = 100 x 1/2 sqrt(2) = 50 sqrt(2) = 70.711 (rounded)
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vectors
If the initial velocity is v, at an angle x to the horizontal, then the vertical component is v*sin(x) and the horizontal component is v*cos(x).
The answer below assumes you are required to find the components of the vector. A vector with unity magnitude means that the magnitude of the vector equals to 1. Therefore its a simple case of calculating the values of sin(45) for the vertical components and cos(45) for the horizontal components. Both of these values equal to 1/sqrt(2) {one over square-root two}
Vertical is up and horizontal is across