The pebble's speed varies based on its initial direction of motion; horizontally it has a constant horizontal velocity throughout its fall, vertically upwards it decelerates then accelerates back down, and vertically downwards it continuously accelerates downwards under gravity.
To find the speed at which the pebble strikes the ground when fired from a building, we must analyze projectile motion and free fall in the context of physics. We ignore air resistance in our calculations.
(a) Horizontal launch:
The initial vertical velocity component is 0 m/s. The pebble falls under gravity and takes √t = √(2h/g) to reach the ground, accelerating at 9.8 m/s². Its horizontal velocity remains 14.0 m/s.
(b) Upward launch:
The pebble's initial velocity is 14.0 m/s upward. It will rise, stop, then fall back down, doubling the time it takes to reach the maximum height. This time is found via t = v/g. The final velocity on hitting the ground is calculated with v² = u² + 2gh.
(c) Downward launch:
Firing the pebble downward adds its initial velocity to the velocity gained while falling under gravity. Again, we use v² = u² + 2gh.
For case (a), the speed is calculated using the Pythagorean theorem. For cases (b) and (c), we find the time to rise and fall, then use it to calculate the final velocity.