To find the maximum height traveled by the stone, we can use the equations of motion for vertical motion under constant acceleration. In this case, the acceleration is due to gravity, and its value is approximately 9.8 m/s² (assuming no air resistance).
We'll convert the initial velocity from kilometers per hour (km/hr) to meters per second (m/s) since the standard unit for acceleration is meters per second squared (m/s²).
Given: Initial velocity (u) = 72 km/hr
First, let's convert the initial velocity to m/s: 1 km/hr = 1000 m/3600 s ≈ 0.2778 m/s u = 72 km/hr * 0.2778 m/s = 20 m/s (approximately)
Using the equation for vertical motion:
v² = u² + 2as
At the maximum height, the final velocity (v) is 0 m/s since the stone momentarily stops before falling back down. The acceleration (a) is -9.8 m/s² (downward), and we want to find the distance traveled (s).
Substituting the known values into the equation:
0² = (20 m/s)² + 2 * (-9.8 m/s²) * s
Simplifying the equation:
0 = 400 m²/s² - 19.6 m/s² * s
Rearranging the equation to solve for s:
19.6 m/s² * s = 400 m²/s²
s = 400 m²/s² / 19.6 m/s²
s ≈ 20.41 meters
Therefore, neglecting air resistance, the stone reaches a maximum height of approximately 20.41 meters.