So-called volcanic 'ash' is actually finely pulverized rock blown high into the atmosphere. A typical ash particle is a 50-micrometer-diameter piece of silica with a density of 2400 kg/m^3. (b) How long in hours does it take this ash particle to fall from a height of 5.0 km in still air? Use the properties of 20°C air at sea level.

Video transcript

Hey, everyone. So this problem has a plastic rod falling from a bucket at a height of 700 m above the ground. The rod's diameter is given as eight millimeters and its length is 35 centimeters. We're also to determine how long it will take the metal rod to hit the ground. And that time they'd like it in hours. So our multiple choice answers here are a 3.32 times 10 to the minus three hours. Four point B is 4.86 times 10 to the minus three hours. Answer choice C is 2.63 times 10 to the minus four hours. And answer choice D Is 5.2, 9 times 10 to the -4 hours. All right. So this is a pretty straightforward kinematics problem. And so the first thing we need to do from our kinematics equations is recall that our distance D as a function of velocity and acceleration is given by V I T plus one half A T squared. We know the distance that was traveled by this rod was m from the problem. We know that the initial velocity Was zero because it was at rest. And we know our acceleration, it's a free fall. So the only acceleration that is acting on this rod is gravity and that is a constant, we can recall 9.8 m per second squared. So we're asked to solve for time and we have all of the other variables. So from here, we can just plug and chug and solve for time. So that looks like we can simplify this. We know that our initial velocity is zero. So that whole first term just goes away. And so D equals one half A T squared. And so T is going to equal the square root Of two D over a. And from there, we can plug in Are known values. So we have distance of 700 m and an acceleration of 9.8 m/s squared. We plug that into our calculator and we get 11.95 seconds. So the last step for this problem is because they asked for us to answer it in hours, not seconds. And so we can recall that There are 3600 seconds in an hour. And so when we plug that in, we get 3.3, 2 Times 10 to the - hours. And so we look at our potential answer choices and that aligns with answer choice. A, so A is the correct answer for this problem. All right, that's all we have for this one. We'll see you in the next video.