Robin Hood wishes to split an arrow already in the...

Robin Hood wishes to split an arrow already in the bull's-eye of a target $40 \mathrm{m}$ away. If he aims directly at the arrow, by how much will he miss? The arrow leaves the bow horizontally at $40 \mathrm{m} / \mathrm{s}$.

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Key Concepts

Projectile Motion

This concept describes the motion of an object that is launched into the air and moves under the influence of gravity. In projectile motion, horizontal motion and vertical motion are treated as independent, with gravity affecting only the vertical component.

Independence of Horizontal and Vertical Motion

The independence principle holds that the horizontal and vertical components of a projectile's motion do not affect each other. While the horizontal velocity remains constant (ignoring air resistance), the vertical velocity increases due to gravity, which leads to a drop in the object's vertical position.

Kinematics under Constant Acceleration (Free Fall)

In problems involving free fall, the vertical displacement of an object is determined using the constant acceleration due to gravity. This is commonly calculated using the formula for displacement (1/2)g t², where t represents the time the object has been falling.

Time of Flight Calculation

The time of flight in a projectile problem can be determined by dividing the horizontal distance by the constant horizontal velocity. This time is then used in the vertical motion calculations to find how far the object drops due to gravity.

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