How many drops per second keeps the protagonist awake? answer check

[negation]

Homework Statement

Your roommate is an aspiring novelist and asks your opinion on a matter of physics. The novel's central character is kept awake at night by a leaky faucet. The sink is 19.6cm below the faucet. At the instant one drop leaves the faucet, another strikes the sink below and two more are in between on the way down. How many drops per second are keeping the protagonist awake?

Homework Equations

None

The Attempt at a Solution

 

[voko]

You had a couple of slips in labeling units correctly, but that did not affect the final result, which is correct.

 

[negation]

You had a couple of slips in labeling units correctly, but that did not affect the final result, which is correct.

Like where 980ms^-2 should be 980cms^-2.

 

[voko]

That is one.

Another is where you calculate how many frames you have in one second. Obviously, the dimension of that is s^-1.

 

[HalfLostAndSearching]

To calculate the number of drops per second, we need to know the time it takes for a drop to travel from the faucet to the sink. This can be calculated using the equation d = 1/2gt^2, where d is the distance (19.6cm), g is the acceleration due to gravity (9.8 m/s^2), and t is the time. Solving for t, we get t = √(2d/g) = √(2*0.196/9.8) = 0.2 seconds.

Since there are 4 drops in this time period, the number of drops per second is 4/0.2 = 20 drops per second. This means that 20 drops are hitting the sink every second, keeping the protagonist awake. However, this number may vary depending on the size of the drops and the rate at which they are dripping from the faucet.