A ball, P, is released from the roof of a building at the same time as another ball, Q, is thrown vertically…

Analyze the question: Two balls are moving under gravity alone. P is dropped from the roof, and Q is thrown upward from the ground. We are asked to compare their accelerations.

Concept: Any object in free fall near Earth's surface, ignoring air resistance, has the same acceleration, g ≈ 10 m/s² (or 9.8 m/s²), directed downward towards the Earth's centre. This holds whether the object is moving up, moving down, or momentarily at rest. The direction of velocity can differ from the direction of acceleration.

Solution:

• Ball P: released from rest and moves downward. Its velocity is downward and its acceleration is g downward.
• Ball Q: thrown upward. It slows down as it rises, stops momentarily at its highest point, then falls. Its velocity is first upward and then downward, but gravity acts on it the whole time, so its acceleration is g downward. The upward motion is deceleration (retardation), not an upward acceleration.

So:

• Magnitude: a_P = a_Q = g (equal)
• Direction: both downward (same direction)

Checking the options:

• A: Wrong, the accelerations are not different.
• B: Wrong, for the same reason.
• C: Correct. The accelerations are equal and in the same direction.
• D: Wrong, the accelerations are not in opposite directions. Only the velocities are opposite at the start.

Answer: C.

Exam tip: Don't confuse velocity with acceleration. In free fall, the acceleration is always g downward, no matter which way the object is moving. If a question says "ignoring air resistance," every object in free fall has the same acceleration.