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The distance traveled by the arrow and horizontal velocity are directly proportional, thus when the distance increases, an increase in initial velocity will allow the arrow to hit the target.
If the horizontal distance the projectile would travel before hitting the target is 70.67 m, the time of motion of the projectile is calculated as;
X = Vx(t)
t = X/Vx
t = X/Vcosθ
t = (70.67) / (45 x cos10)
t = 1.6 s
When the archery target is moved further away from the archer, the archer needs increase the initial velocity of the arrow assuming the angle of projection is constant.
Since the distance and horizontal velocity are directly proportional to each other, thus when the distance increases, an increase in initial velocity will allow the arrow to hit the target.
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