To find the time it takes for the stone to reach the maximum height, we can use the fact that at the maximum height, the vertical component of velocity becomes zero.
Given: Initial velocity (u) = 25 m/s Final velocity (v) = 0 m/s (at maximum height) Acceleration due to gravity (g) = -9.8 m/s² (taking the downward direction as negative)
Using the kinematic equation for vertical motion: v = u + at
At the maximum height, v = 0 m/s, so we can rearrange the equation as follows: 0 = 25 m/s + (-9.8 m/s²)t
Solving for t, we have: 9.8 m/s²t = 25 m/s t = 25 m/s / 9.8 m/s² t ≈ 2.55 seconds
Therefore, it takes approximately 2.55 seconds for the stone to reach the maximum height.
To calculate the height, we can use another kinematic equation:
s = ut + (1/2)at²
where: s = height (unknown) u = initial velocity = 25 m/s t = time taken to reach the maximum height = 2.55 seconds a = acceleration due to gravity = -9.8 m/s²
Substituting the values, we get: s = (25 m/s)(2.55 s) + (1/2)(-9.8 m/s²)(2.55 s)² s ≈ 31.88 meters
Therefore, the maximum height reached by the stone is approximately 31.88 meters.
Now, to determine the time it takes for the stone to hit the ground, we can use the fact that the initial vertical velocity (25 m/s) will become negative (-25 m/s) since it's moving downwards.
Using the same kinematic equation: v = u + at
Given: u = 25 m/s v = -25 m/s a = -9.8 m/s²
Rearranging the equation: -25 m/s = 25 m/s + (-9.8 m/s²)t
Solving for t: -9.8 m/s²t = -50 m/s t = -50 m/s / -9.8 m/s² t ≈ 5.10 seconds
Therefore, it takes approximately 5.10 seconds for the stone to hit the ground.
Note: In this calculation, we assume negligible air resistance.