v = 20 - 9.81 t
v = 0 at top
t = 20/9.81= 2.04 seconds upward
h = average speed up * time = 10 * 2.04 = 20.4 meters up
v = 0 at top
t = 20/9.81= 2.04 seconds upward
h = average speed up * time = 10 * 2.04 = 20.4 meters up
t = Vf / g
Where t is the time, Vf is the final velocity (which is 0 at the top), and g is the acceleration due to gravity. In this case, the initial velocity of the stone is 20 m/s, so Vf would be 0. Plus, we'll assume that g is approximately 9.8 m/s². Plugging these values into the equation, we get:
t = 0 / 9.8
Since anything divided by 9.8 is 0, we can conclude that the time it takes for the stone to reach the top is 0 seconds. Therefore, it doesn't take any distance to reach the top since it happens instantaneously.
displacement = (initial velocity^2) / (2 * acceleration)
In this case, since the stone is thrown upwards, the acceleration due to gravity acts in the opposite direction, which is -9.8 m/s^2 (taking the negative sign to indicate the opposite direction).
Let's calculate the displacement:
displacement = (initial velocity^2) / (2 * acceleration)
displacement = (20 m/s)^2 / (2 * -9.8 m/s^2)
Using a calculator, the displacement is:
displacement ≈ 20.41 meters
So, it takes approximately 20.41 meters for the stone to reach the top.
The equation for displacement (d) is given by:
d = v₀t + (1/2)gt²
Where:
- vâ‚€ is the initial velocity
- t is the time taken
- g is the acceleration due to gravity, which is approximately 9.8 m/s² on Earth
In this case, the initial velocity (vâ‚€) is 20 m/s and we need to find the time taken to reach the top (t). At the maximum height, the final velocity will be zero, so we can use that information to solve for t.
We can rearrange the equation to solve for time (t):
0 = vâ‚€ - gt
Rewriting it:
t = vâ‚€/g
Plugging in the values:
t = 20 m/s / 9.8 m/s²
Calculating t:
t ≈ 2.04 seconds
Therefore, it takes approximately 2.04 seconds for the stone to reach the top.
Note: This calculation is based on the assumption of no air resistance.