Question

What is the size of cough and sneezing droplets and how far they can travel? (try to calculate the distance and give reference of scientific studies only. You can use video or images to explain your answer wherever needed)

Answer 1

the problem is based on the concepts of the motion under gravity.

when a person coughs or sneezes the cough particles comes out of a persons mouth and then fall under gravity as well as moves in the horizontal direction too. this type of motion is called projectile motion.

from the study we take the average values of,

the size of the cough particles approximately have of diameter.

average height of human being's mouth from the ground = 1.7 m

it is found by study that cough particles comes out of mouth with velocity = 10 m/s

hence the motion diagram will look like,

there will be motion in horizontal direction and vertical direction.

the vertical motion will be under the influence of the acceleration due to gravity

and the horizontal motion will not be under any acceleration.

hence

we know the equation of motion as,

so,

for the y direction motion,

y = 1.7 m

g = -9.8 m/s2 (minus sign because the direction of g is in negative direction of y)

and v = 0 in y direction.

so,

we get

we get

we get

............ (1)

so, the cough articles will remain in air for around 0.588 sec.

now the motion in x direction,

g = 0

v = 10 m/s

and we have obtained time = t =0.588 sec

so,

so,

we get

.......... {ans.}

so the particle will move till 5.88 m from the person.

in feet units.

x = 5.88 m * 3.28084 ft /1m = 19.29134 ft........... {ans}

so,

the particle will move 19.29 ft from the person.

the answer is based on the scientific studies and it is approximate.