A acorn falls from a tree and hits the ground with a speed of 10 m/s:
- From what height did the acorn fall?
- How long was the acorn in the air?
If the acorn fell from rest,
equate energies
mgh=(1/2)mv²
h=v²/2g
=100/(2*9.8)
=5.1 m
Time
=v/g
=10/9.8
=1.02 s
To find the height from which the acorn fell, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the acorn comes to rest on the ground)
u = initial velocity (10 m/s)
a = acceleration (acceleration due to gravity, which is approximately 9.8 m/s^2)
s = displacement or height
Rearranging the equation:
s = (v^2 - u^2) / (2a)
s = (0^2 - 10^2) / (2*(-9.8))
s = -100 / (-19.6)
s ≈ 5.1 meters
Therefore, the acorn fell from a height of approximately 5.1 meters.
To find how long the acorn was in the air, we can use the equation:
v = u + at
Where:
v = final velocity (0 m/s)
u = initial velocity (10 m/s)
a = acceleration (acceleration due to gravity, which is approximately 9.8 m/s^2)
t = time
Rearranging the equation:
t = (v - u) / a
t = (0 - 10) / (-9.8)
t ≈ 1.02 seconds
Therefore, the acorn was in the air for approximately 1.02 seconds.
To determine the height from which the acorn fell, we can use the kinematic equation of motion:
v² = u² + 2as
Where:
v = final velocity (0 m/s on the ground)
u = initial velocity (10 m/s)
a = acceleration due to gravity (-9.8 m/s², assuming no air resistance)
s = height
Rearranging the equation gives us:
s = (v² - u²) / (2a)
Substituting the values:
s = (0² - 10²) / (2 * -9.8)
s = (-100) / (-19.6)
s = 5.102 m
Therefore, the acorn fell from a height of approximately 5.102 meters.
To determine how long the acorn was in the air, we can use another kinematic equation:
v = u + at
Where:
v = final velocity (0 m/s on the ground)
u = initial velocity (10 m/s)
a = acceleration due to gravity (-9.8 m/s²)
Rearranging the equation gives us:
t = (v - u) / a
Substituting the values:
t = (0 - 10) / -9.8
t = 10 / 9.8
t = 1.02 seconds
Therefore, the acorn was in the air for approximately 1.02 seconds.