Using the projectile motion formula Range = (v^2 × sin(2θ)) / g, what is the range when θ = 0?

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Multiple Choice

Using the projectile motion formula Range = (v^2 × sin(2θ)) / g, what is the range when θ = 0?

Explanation:
The range is tied to the horizontal distance the projectile covers, which in the formula is scaled by sin(2θ). When the launch angle is zero, the double angle is zero, and sin(0) = 0, so the range becomes zero regardless of speed or gravity. Physically, launching along the ground means there’s no initial vertical velocity to lift the projectile, so it doesn’t stay in the air long enough to move horizontally on level ground. The result matches intuition: without any upward component, there’s no time aloft to generate horizontal displacement.

The range is tied to the horizontal distance the projectile covers, which in the formula is scaled by sin(2θ). When the launch angle is zero, the double angle is zero, and sin(0) = 0, so the range becomes zero regardless of speed or gravity. Physically, launching along the ground means there’s no initial vertical velocity to lift the projectile, so it doesn’t stay in the air long enough to move horizontally on level ground. The result matches intuition: without any upward component, there’s no time aloft to generate horizontal displacement.

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