To solve this problem, we can use the equations of motion for an object thrown vertically upwards. Let's calculate the velocity, maximum height, and time taken to reach the maximum height.
- Velocity: The initial velocity (u) is 80 m/s, and the final velocity (v) at the maximum height will be 0 m/s since the stone momentarily comes to rest before starting to fall back down.
We can use the equation: v = u + at
Where: v = final velocity (0 m/s) u = initial velocity (80 m/s) a = acceleration (due to gravity, approximately -9.8 m/s²) t = time
Rearranging the equation, we have: 0 = 80 - 9.8t
Solving for t: 9.8t = 80 t = 80 / 9.8 t ≈ 8.16 seconds
Therefore, it takes approximately 8.16 seconds for the stone to reach its maximum height.
- Maximum Height: To find the maximum height (h), we can use the equation: h = ut + (1/2)at²
Substituting the known values: h = (80)(8.16) + (1/2)(-9.8)(8.16)²
Simplifying: h ≈ 326.4 - 319.5 h ≈ 6.9 meters
Therefore, the maximum height reached by the stone is approximately 6.9 meters.
- Time taken to reach the maximum height: We have already determined that the time taken to reach the maximum height is approximately 8.16 seconds.
In summary:
- Velocity at the maximum height is 0 m/s.
- The maximum height reached by the stone is approximately 6.9 meters.
- It takes approximately 8.16 seconds to reach the maximum height.