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Answer:
His new horizontal range is 4 times his initial range.
Explanation:
Since Mike serves the ball with velocity, u, his horizontal range is
R = u²sin2Ф/g where Ф is the angle between u and the horizontal.
Now, if on his second serve, the ball leaves his hand with twice the velocity of his initial serve, the new velocity is v = 2u.
So, the new range R' = v²sin2Ф/g
R' = (2u)²sin2Ф/g
R' = 4u²sin2Ф/g
Since R = u²sin2Ф/g,
R' = 4u²sin2Ф/g
R' = 4R
So, his new horizontal range is 4 times his initial range.