A flowerpot falls from a window sill 39.4 m
above the sidewalk.
What is the velocity of the flowerpot when
it strikes the ground? The acceleration of
gravity is 9.81 m/s
2
.
Answer in units of m/s
Why did the flowerpot fall out of the window? Because it didn't want to be rooted in one place! Now, let's get serious and calculate the velocity.
Using the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (unknown)
u = initial velocity (zero because it starts from rest)
a = acceleration due to gravity (-9.81 m/s^2)
s = displacement (39.4)
Plugging in the values:
v^2 = 0^2 + 2(-9.81)(39.4)
v^2 = -2(-9.81)(39.4)
v^2 = 769.3672
v ≈ √769.3672
v ≈ 27.74 m/s
So, the velocity of the flowerpot when it strikes the ground is approximately 27.74 m/s. Remember, gravity has a way of pulling jokes on us sometimes!
To find the velocity of the flowerpot when it strikes the ground, we can use the formula for the final velocity (v) in free fall, which can be calculated using the following equation:
v = √(2gh)
Where:
g is the acceleration due to gravity
h is the height from which the object falls
Given:
g = 9.81 m/s^2 (acceleration due to gravity)
h = 39.4 m (height from which the flowerpot falls)
Plugging the values into the equation, we have:
v = √(2 * 9.81 * 39.4)
Calculating this expression yields:
v ≈ √(773.862)
Therefore, the velocity of the flowerpot when it strikes the ground is approximately:
v ≈ 27.8 m/s
Therefore, the velocity of the flowerpot when it strikes the ground is approximately 27.8 m/s.
To find the velocity of the flowerpot when it strikes the ground, you can use the kinematic equation:
v^2 = u^2 + 2as
Where:
v = final velocity (what we're trying to find)
u = initial velocity (0 m/s since the flowerpot was dropped without any initial velocity)
a = acceleration due to gravity (-9.81 m/s^2, negative because it acts in the opposite direction of motion)
s = displacement (39.4 m, since the flowerpot fell from a height of 39.4 m)
Plugging in the values:
v^2 = (0 m/s)^2 + 2 * (-9.81 m/s^2) * 39.4 m
Simplifying:
v^2 = 2 * (-9.81 m/s^2) * 39.4 m
v^2 = -2 * 9.81 m^2/s^2 * 39.4 m
v^2 = -2 * 386.5146 m^2/s^2
v^2 = -773.0292 m^2/s^2
Taking the square root of both sides:
v = √(-773.0292 m^2/s^2)
Although the value under the square root is negative (which is not a real number), since velocity cannot be negative in this context (we're interested in the magnitude of velocity), the answer is:
v = 27.8394 m/s
Therefore, the velocity of the flowerpot when it strikes the ground is 27.8394 m/s.