A pot with a flower falls out of a window box in a tall apartment building. It passes the top of a particular window with a velocity of -1.7 m/s. It passes the bottom of this window 0.2800 s later? How tall is the window (watch sign)?
the numbers are different: same exact problem though
In order to find the distance between the the bottom of the window above which is where the flowerpot was dropped(window 1) to the top of the window below (window 2) we need to find the velocity of the flowerpot as it passes the top of the window. Later this will serve as our "V-final." We know three things which is all you need to solve kinematic equations. 1) the distance the flowerpot travels = 2.2. 2) The time it took for the pot to travel 2.2 m= 0.3 seconds. 3) since this is a free fall problem acceleration and the flower pot is falling in the Y-direction ay = +9.8
we use this to solve for Voy at the top of the window 2
y=y0 + V0yt * 1/2ayt^2
Isolate Voy:
V0y= Dy/t - 1/2ayt
V0y=2.2/0.3 - 1/2*9.8*o.3 = 5.86 m/s
now that you have your V-initial, V0: solve for the distance between window 1 and window 2. We know three things: 1) since the flowerpot appears to have started from rest the initial velocity is zero and the initial velocity you just found becomes your finally velocity since you are finding the distance from the bottom of window one to the top of window two. 2) free fall problem = acceleration = 9.8, 3) final velocity = 5.86 m/s
now use kinematic equation to solve for distance delta-y or "Dy"
Vf^2 = V0^2 + 2*ay*Dy
Dy = (Vf^2 - V0^2)/ 2*ay
Dy = (5.86^2 - 0)/ 2 * 9.8 = 1.75 m
Vf is final velocity
V0 is initial velocity
Dy or Delta Y refers to the change in y or displacement. Change is y is similar to change in X. they are both displacement vectors but along a different axis or direction which is why it is very important to know the difference when your solving a physics problem. is the displacement occuring in the X- or Y- direction?
To find the height of the window, we first need to find the distance traveled by the pot during the 0.2800 seconds between passing the top and bottom of the window.
We can use the equation of motion to calculate this distance. The equation of motion in this case is:
distance = initial velocity × time + (1/2) × acceleration × time^2
In this case, the initial velocity is -1.7 m/s (negative because it's moving downward), the time is 0.2800 seconds, and since the acceleration is due to gravity, we can use a value of 9.8 m/s^2.
Plugging the values into the equation, we have:
distance = -1.7 m/s × 0.2800 s + (1/2) × 9.8 m/s^2 × (0.2800 s)^2
Simplifying the equation, we get:
distance = -0.476 m + 0.3896 m
distance = -0.0864 m
The negative sign indicates that the pot is moving downward. Therefore, the distance traveled by the pot during the 0.2800 seconds is 0.0864 meters.
Now, to find the height of the window, we need to consider that the pot passed the top and bottom of the window during this time. So, the height of the window is equal to twice the distance traveled by the pot:
height of window = 2 × 0.0864 m
height of window = 0.1728 m
Thus, the height of the window is 0.1728 meters.