To find the maximum height reached by the stone and the time taken to reach that height, we can use the equations of motion and consider the vertical motion of the stone.
Given: Initial velocity, u = 20 m/s (upward) Acceleration due to gravity, g ≈ 9.8 m/s² (downward)
- Maximum Height: At the maximum height, the final velocity of the stone will be zero (as it momentarily stops before falling back down). We can use the following equation of motion to find the maximum height (h):
v² = u² + 2as
where:
- v is the final velocity (which is 0 at the maximum height)
- u is the initial velocity
- a is the acceleration (which is -g, considering downward acceleration due to gravity)
- s is the displacement (maximum height, h)
0² = (20 m/s)² + 2(-9.8 m/s²)h
Simplifying the equation:
0 = 400 m²/s² - 19.6h
19.6h = 400 m²/s²
h = (400 m²/s²) / 19.6 m/s² h ≈ 20.41 meters
Therefore, the maximum height reached by the stone is approximately 20.41 meters.
- Time taken to reach the maximum height: To find the time taken by the stone to reach the maximum height, we can use the following equation of motion:
v = u + at
Since the final velocity (v) at the maximum height is 0, we can rearrange the equation as follows:
0 = u + gt
Solving for t:
t = -u / g t = -20 m/s / -9.8 m/s² t ≈ 2.04 seconds
Therefore, the time taken by the stone to reach the maximum height is approximately 2.04 seconds.