You explore the horizontal range of a projectile in a Physics 211 lab experiment on 2D kinematics. The projectile is launched from a tabletop and returns to the same tabletop altitude. Neglecting air resistance, which statement is true?

Question

BlackTom AI · Accepted Answer

The question describes a projectile launched from a tabletop and returning to the same tabletop altitude in a vacuum (no air resistance) in a 2D kinematics setup. In this standard scenario, the horizontal range (distance traveled before returning to the same height) is governed by the range formula R = v0^2 sin(2θ) / g, where v0 is the launch speed, θ is the launch angle relative to the horizontal, and g is the acceleration due to gravity.

Option analysis:
- If we consider the general result R = v0^2 sin(2θ) / g, the sine term sin(2θ) achieves its maximum value of 1 when 2θ = 90°, i.e., θ = 45°. Therefore, the range is maximized at a 45° launch angle on level ground with no air resistance, assuming the initial and final heights are equal, as stated in the question.
- If there were other possible statements about the launch angle, one would test them against the same range expression. For instance, angles less than 45° produce smaller sin(2θ) values, yielding shorter ranges; angles greater than 45° produce the same range as their complementary angle (since sin(2θ) = sin(180°−2θ)), but in practice the maximum is at 45° because that maximizes sin(2θ).

Potential edge considerations:
- If the launch and landing heights were different, the angle that maximizes range would not be exactly 45°, and the simple sin(2θ) form would need to be combined with height differences in the full range equation.
- If air resistance were not neglected, the optimal angle would deviate from 45°, and the maximum range would generally occur at an angle somewhat less than 45° depending on the drag model.

Given the standard textbook result for a projectile launched from and landing at the same height with no air resistance, the statement that the maximum range occurs at a 45° launch angle aligns with the established theory.

Note: The provided options field is empty in this dataset, so no explicit choice can be selected here. The reasoning above explains why, if the option were present, the 45° choice would be the correct one under the stated conditions.

Section Merge: PHYS 211: Mechanics (UP; Spring 2025) Phys211_MT1

You explore the horizontal range of a projectile in a Physics 211 lab experiment on 2D kinematics. The projectile is launched from a tabletop and returns to the same tabletop altitude. Neglecting air resistance, which statement is true?

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