A teacher drops a steel ball from a window 4.9 m above the ground. Fig. 7.1 shows the arrangement. The ball is released from rest and air resistance is negl...

(a) The acceleration of free fall is the acceleration experienced by an object falling freely under gravity near the Earth's surface, with no other forces acting (such as air resistance). Its value is approximately \( 9.8\text{ m/s}^2 \). [1]

All objects in free fall (regardless of mass) accelerate at this rate, provided air resistance is negligible. This was famously demonstrated by Galileo and later confirmed on the Moon by Apollo astronauts.

(b) Speed after 0.50 s: [2]

The ball starts from rest (\( u = 0 \)), so:

\[ v = u + gt = 0 + 9.8 \times 0.50 \] [1]

\[ = 4.9\text{ m/s} \] [1]

(c) Speed after 1.0 s (just before hitting the ground): [2]

\[ v = u + gt = 0 + 9.8 \times 1.0 \] [1]

\[ = 9.8\text{ m/s} \] [1]

We can verify this is consistent with the height: \( s = \frac{1}{2}gt^2 = \frac{1}{2}(9.8)(1.0)^2 = 4.9 \) m, which matches the 4.9 m drop height.

(d) Air resistance is negligible because the ball is small and dense (heavy for its size), so the drag force is very small compared to its weight. [1]

Additionally, the fall distance is short (4.9 m) and the ball does not reach a high speed, so air resistance never builds up to a significant fraction of the gravitational force.

(e) One method to measure the time of fall accurately: use an electronic timer triggered by a switch at the release point and stopped by a sensor pad on the ground. [1]

This eliminates human reaction time error, which would be a large fraction of the approximately 1.0 s fall time. Alternatively, slow-motion video recording could be used to observe the exact start and end of the fall.