3. A person throws a ball across a field. When the ball is at the highest point of its
trajectory, the direction of its velocity and acceleration are
a. parallel to each other
b. anti-parallel to each other
c. inclined to each other at an angle of 45°
d. 90° to each other
Correct Answer
Answer: d. 90° to each other
At the highest point of a projectile’s trajectory, the ball’s velocity is purely horizontal while its acceleration due to gravity is vertical downward, making them perpendicular.
Option Analysis
- a. Parallel to each other: Incorrect. Parallel vectors point in the same direction, but horizontal velocity and downward acceleration never align.
- b. Anti-parallel to each other: Incorrect. Anti-parallel means opposite directions (180°), which does not match the horizontal-vertical relationship.
- c. Inclined to each other at an angle of 45°: Incorrect. No 45° angle exists; the directions are exactly orthogonal.
- d. 90° to each other: Correct. Velocity has zero vertical component (vy = 0), leaving only horizontal (vx); acceleration is g downward.
Projectile Motion Basics
In projectile motion, the initial velocity splits into horizontal (vx = v₀cosθ) and vertical (vy = v₀sinθ) components. The horizontal velocity remains constant (ignoring air resistance). The vertical velocity becomes zero at the peak:
vy = 0 = v₀sinθ − gt, hence t = v₀sinθ / g.
Acceleration remains ⃗a = −gĵ (downward).
Introduction to Ball Trajectory Physics
When a person throws a ball across a field, it follows a parabolic path under gravity. The ball’s highest point of trajectory marks where vertical motion reverses. Here, velocity is horizontal and acceleration vertical — perpendicular at 90°.
Velocity and Acceleration Directions
At the apex:
- Vertical velocity component becomes zero while the horizontal component persists.
- Acceleration due to gravity acts solely downward (g ≈ 9.8 m/s²).
Vectors: ⃗v = vxî, ⃗a = −gĵ. The dot product ⃗v ⋅ ⃗a = 0 confirms perpendicularity.
Summary:
- Horizontal velocity remains unchanged.
- Vertical velocity becomes zero.
- Acceleration stays constant and downward.
Common Exam Misconceptions
Students often confuse this with a vertical throw, where velocity and acceleration are both vertical (velocity zero, acceleration downward). For an angled projectile, velocity never fully vanishes at the peak. Options like “parallel” or “45°” fail under vector analysis.
Practical Implications
This principle applies in sports, ballistics, and animation physics. Time to reach the peak is given by:
t = v₀sinθ / g
Maximum height achieved:
h = (v₀²sin²θ) / (2g)
