In ideal projectile motion (neglecting air resistance), an object launched horizontally from a height will follow which path?

• A. A parabolic trajectory
• B. A vertical line straight downward
• C. A circular arc with constant radius
• D. A straight-line path at constant speed

Answer: (A)

Verified step by step guidance

1. Understand that in ideal projectile motion, the only force acting on the object after launch is gravity, which acts vertically downward.
2. Since the object is launched horizontally, its initial vertical velocity is zero, but it has a constant horizontal velocity because there is no air resistance.
3. The vertical motion is uniformly accelerated motion due to gravity, described by the equation \(y = \frac{1}{2} g t^{2}\), where \(g\) is the acceleration due to gravity and \(t\) is time.
4. The horizontal motion is uniform, described by \(x = v_{0} t\), where \(v_{0}\) is the initial horizontal velocity.
5. Combining the horizontal and vertical motions, the path of the object is given by eliminating \(t\) to get \(y = \frac{g}{2 v_{0}^{2}} x^{2}\), which is the equation of a parabola, showing the object follows a parabolic trajectory.