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A soccer player kicks a ball toward a net. Which statement correctly explains how far the ball will travel?
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The distance the ball travels is set by its initial speed and launch angle because the horizontal and vertical motions are independent. Gravity accelerates the ball downward and controls the time it spends in the air (vertical motion), while—neglecting air resistance—the horizontal component of its velocity stays essentially constant and determines how far it moves while aloft.
For an ideal projectile launched and landing at the same height, the range is
R = v^2 sin(2θ) / g,
so for a given launch speed v the maximum range occurs at θ = 45°. In the real world air resistance, spin (Magnus effect), and different launch/landing heights will change the distance.
For an ideal projectile launched and landing at the same height, the range is
R = v^2 sin(2θ) / g,
so for a given launch speed v the maximum range occurs at θ = 45°. In the real world air resistance, spin (Magnus effect), and different launch/landing heights will change the distance.
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