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. (a) How long would it take this ash particle to fall from a height of 5.0 km in vacuum?

Video transcript

Everyone in this practice problem, we're being asked to calculate the time that it takes for a ball to fall from a height of 2.5 m. We will have a ball made out of metal which will have a diameter of 0.3 m. And the options given for the time are a 0. seconds. B 0.71 seconds, C 0.55 seconds and D 0.78 seconds. So in order for us to solve this problem, we want to use the second equation of motion to find the time that it takes for the ball to fall from a height of 2.5 m. So the second equation of motion will be given by delta Y equals to V I multiplied by T plus half, multiplied by A Y multiplied by T squared. In this case, as the ball is free falling, then we know that the A Y or the vertical acceleration is just going to equals to the gravitational acceleration considering the reference frame such as down is positive and up is negative. We don't have a negative sign in front of the G here because of that reference frame of anything going downwards to be positive. So um it is also assumed that the ball will start its motion from rest. So therefore, our V I will then equals to zero m per second. So thus, equation, this equation that we have will then become delta Y equals to 04 V I multiplied by T will also equals to zero plus half multiplied by A Y A Y is gonna be R G multiply that by T squared. So then delta Y will then equals to half multiplied by G multiplied by T squared just like. So, so what we're interested to find is the time. So we want to rearrange this in order for us to get an equation for time or T, which will then equals to the square root of two multiplied by delta Y divided by G just like. So, so that is the final equation that we have for the time. So now we can actually substitute all of the given information in the problem statement in order for us to calculate the time. So first we have delta Y which is just going to be 2.5 m. So we have the square root of two multiply that by 2.5 m. And we want to divide that by G which is going to be 9. m per second squared. Calculating this, it will give us the time that it takes for the ball to fall from the 2.5 m height, which will be 0.71 seconds. So 0.71 seconds will be the answer to this practice problem which will correspond to option B in our answer choices. So option B will be the answer to this problem and that'll be it for this video. If you guys still have any sort of confusion, please make sure to check out our other lesson videos on similar topics and that'll be it for this one. Thank you.