A stone with a mass of 6kg is thrown vertically upwards from the top of the building 35m high with a starting velocity 20m/s .
Determine the time it will take the stone to reach it's maximum height.
gravity slows the stone 9.8 m/s for every second of upward flight
... the stone stops at max height and begins to fall back down
time to max is ... (20 m/s) / (9.8 m/s^2)
To determine the time it will take for the stone to reach its maximum height, we need to use the following kinematic equation:
vf = vi + at
Where:
- vf is the final velocity (at maximum height)
- vi is the initial velocity (20 m/s)
- a is the acceleration (in this case, the acceleration due to gravity, approximately 9.8 m/s^2)
- t is the time we're trying to find
At the maximum height, the final velocity will be 0 m/s because the stone momentarily comes to a stop before falling down. Therefore, we can rewrite the equation as:
0 = 20 - 9.8t
Solving for t, we get:
9.8t = 20
t = 20 / 9.8
t ≈ 2.04 seconds
Therefore, it will take the stone approximately 2.04 seconds to reach its maximum height.