Judy, by chance, spots a potted plant falling
outside the window at 2.04 m/s . Further
down the same building, Judy’s boyfriend
clocks the pot at 56 m/s .
How far apart are the friends? The acceleration of gravity is 9.8 m/s
2
.
d = (Vf^2 - Vo^2) / 2g,
d = ((56)^2 - (2.04)^2) / 19.6 = 159.8m
Well, it seems like Judy's potted plant has decided to take a leap of faith! Thankfully, her boyfriend was there to catch all the action. Now, to calculate the distance between the two friends, we'll need to do a little math (don't worry, I'll make it as painless as possible).
Let's start with Judy's observation. She noticed the potted plant falling at a velocity of 2.04 m/s. We'll call this velocity "Vj" (short for Velocity Judy, because I like giving fancy names to things).
Now, down the same building, her boyfriend saw the pot speeding at a whopping 56 m/s (that's one fast falling plant!). We'll refer to this velocity as "Vb" (Velocity Boyfriend, if you will).
Since we're dealing with gravity here, we know that the acceleration due to gravity is 9.8 m/s^2. I like to think of it as nature's way of saying, "Hey, everything falls, so let's make it uniform and predictable!"
To calculate the distance between the two friends, we'll use the equation:
d = (Vj^2 - Vb^2) / (2 * g)
Where "d" is the distance, "Vj" is Judy's observed velocity, "Vb" is her boyfriend's observed velocity, and "g" is the acceleration due to gravity.
Now let's plug in the numbers and have some fun!
d = (2.04^2 - 56^2) / (2 * 9.8)
d = (-3143.4) / 19.6
d = -160.32 meters
Uh-oh! It seems like we have a negative distance here. That can't be right! Maybe someone accidentally dropped the pot on a trampoline and it bounced back up. Let's assume that's what happened and take the absolute value of our distance.
|d| = |-160.32| = 160.32 meters
There you have it! The distance between the friends is approximately 160.32 meters. I hope this little physics problem lightened the mood a bit!
To find the distance between the friends, we need to determine the time it takes for the potted plant to fall from the window down to where Judy's boyfriend is standing.
First, let's calculate the time it takes for the plant to fall near Judy's boyfriend using the equation of motion:
v = u + at
Where:
v = final velocity = 56 m/s (velocity at Judy's boyfriend)
u = initial velocity = 0 (as the plant starts falling from rest)
a = acceleration = 9.8 m/s^2 (acceleration due to gravity)
t = time
Rearranging the equation, we have:
t = (v - u) / a
Plugging in the given values:
t = (56 - 0) / 9.8
t = 5.71 seconds (rounded to two decimal places)
Now, we need to calculate the distance traveled by the plant in that time. We'll use the equation of motion:
s = ut + 0.5at^2
Where:
s = distance traveled
u = initial velocity = 0
a = acceleration = 9.8 m/s^2
t = time = 5.71 seconds (rounded from previous calculation)
Plugging in the given values:
s = 0 * 5.71 + 0.5 * 9.8 * (5.71)^2
s ≈ 160.46 meters (rounded to two decimal places)
Therefore, Judy and her boyfriend are approximately 160.46 meters apart.
To find the distance between the friends, we can start by finding the time it takes for the potted plant to reach Judy's boyfriend.
First, let's find the time it takes for the potted plant to reach the ground using the given initial velocity (2.04 m/s) and the acceleration due to gravity (-9.8 m/s^2). We can use the following kinematic equation:
vf = vi + at
In this case, the final velocity (vf) is 0 m/s (at the moment the plant hits the ground), the initial velocity (vi) is 2.04 m/s, and the acceleration (a) is -9.8 m/s^2. We need to solve for time (t).
0 = 2.04 + (-9.8)t
Simplifying the equation:
-2.04 = -9.8t
Dividing both sides by -9.8:
t = -2.04 / -9.8 ≈ 0.208 s
Now we know the time it takes for the potted plant to fall to the ground is approximately 0.208 seconds.
Next, we can calculate the horizontal distance traveled by Judy's boyfriend during this time. We can use the formula:
d = vt
In this case, the velocity (v) is 56 m/s, and the time (t) is 0.208 s.
d = 56 * 0.208
d ≈ 11.648 m
Therefore, Judy and her boyfriend are approximately 11.648 meters apart.