Time for a Droplet of Water to Fall .25m from Hole

[skoopfadj]

Time for Droplet of Water to Fall .25m from Hole

Homework Statement

A cylindrical tank .7m tall is filled with water and placed on a stand (below it) that is .3m tall. A hole of radius .001 m in the bottom of tank is opened. Water then flows through the hole and through an opening in the stand and is collected in a tray .3 m below the hole. At the same time, water is added to the tank at an appropriate rate so that the water level in the tank remains constant.
Find:
^The speed at which the water flows out from the hole
[Done: 3.7 m/s]
^The volume rate at which water flows out from the hole
[Done: 1.1623893 x 10^-5 m³/s]
^The volume of water collected in the tray in 2 minutes
[Done: .0013948672 m³]
^ ! The time it takes for a droplet of water to fall 0 .25 m from the hole.

Homework Equations

Density of Water: 1000 kg/m³

3. The attempt

- PART D -

*The time it takes for a droplet of water to fall 0 .25 m from the hole.
ΔX = V_°*t + (1/2)*a*t²
-
.25 = 3.7t + (1/2)(9.8)t²
-
4.9t² + 3.7t - 0.25 = 0
- Used Quadratic Equation but answer turned out negative and does not match answers -
? ? ?
Correct Answer: 0. 062 seconds
My question is how.

 

[gneill]

4.9t² + 3.7t - 0.25 = 0
- Used Quadratic Equation but answer turned out negative and does not match answers -
? ? ?
Correct Answer: 0. 062 seconds
My question is how.

Show your quadratic formula workings. Something must've gone awry, because I get two results and one of them matches the expected value.

 

[skoopfadj]

I pretty much laid out the whole schema. I know the quadratic equation I provided gives answers that do not match the correct one (as I stated earlier). However, I'm not sure if I'm even supposed to use the kinematics equation listed above in order to solve the problem.
The answer may even be 0.021 seconds but my professor informed me that 0.021 was not the answer and promptly replaced the old answer with 0.062 seconds.

 

[gneill]

I pretty much laid out the whole schema. I know the quadratic equation gives answers that do not match the correct one (as I stated earlier). However, I'm not sure if I'm even supposed to use the kinematics equation listed above in order to solve the problem.

The method is fine. What I'm saying is, something went wrong in your application of the quadratic formula. as I obtained the correct result using the same starting point.

 

[Nickie]

The correct answer for the time it takes for a droplet of water to fall 0.25m from the hole is 0.062 seconds. This can be calculated using the equation d = (1/2)at^2, where d is the distance, a is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Plugging in the values, we get 0.25 = (1/2)(9.8)t^2. Solving for t, we get t = 0.062 seconds.
It is important to note that this equation only works for objects in free fall, where air resistance is negligible. In this case, the droplet of water is in free fall as it falls through the air and then through the hole.
I hope this helps to clarify the answer for you.