Final answer:
The stone reaches a maximum height of about 16.5 meters and returns to the ground with a final velocity of -18.0 m/s, which is equal in magnitude but opposite in direction to the initial velocity.
Step-by-step explanation:
To calculate how high the stone goes when thrown vertically upward with a speed of 18.0 m/s, we will use the formula for vertical motion under constant acceleration due to gravity (assuming no air resistance):
final velocity2 = initial velocity2 + 2 × acceleration × displacement
At its highest point, the stone's final velocity is 0 m/s. The acceleration due to gravity is -9.8 m/s2 (negative because it acts downwards). Using these and rearranging the formula to find displacement (height), we get:
0 = 18.02 + 2 × (-9.8) × height
Solving for height, we find that the stone reaches a maximum height of approximately 16.5 meters.
On its way back down, assuming no air resistance, the stone's velocity when it returns to the ground will be equal in magnitude but opposite in direction to its initial velocity due to the symmetry of the motion in freefall - so the stone's final velocity will be -18.0 m/s.