Question

a student throws a heavy ball downward off the top a building with a speed of 12m/s. the ball increases speed until it strikes the ground and suddenly comes to rest.
determine all unknowns.
$|v_i|$ = 12 m/s
$|v|$ = ___ m/s
$|v_f|$ = 0 m/s

Explanation:

Step1: Identify initial speed

The problem states the initial downward speed of the ball is given as $|v_i| = 12$ m/s, which is already provided.

Step2: Identify final resting speed

When the ball comes to rest on the ground, its final speed is $|v_f| = 0$ m/s, which is already provided.

Step3: Note missing motion data

To find the impact speed $|v|$, we need either the height of the building ($h$) or the time ($t$) the ball falls, as kinematic equations like $v^2 = v_i^2 + 2gh$ require this additional information. Since neither the height nor fall time is given, the impact speed cannot be calculated with the provided data.

Answer:

• $|v_i| = 12$ m/s (given initial speed)
• $|v_f| = 0$ m/s (final resting speed)
• $|v|$ (impact speed) cannot be determined without the height of the building or time of fall.