It was speculated that humans sneeze at speeds of up to 100 mile per hour. The Myth Busters Team of The Discovery Channel got interesting results after testing this speculation. After multiple sneezes, the fasted they were able to record was a sneeze speed of 39 mph. The person who sneezed this speed was 6 feet tall.
Calculating
booger travel distance:
Kinematics!!!
Vo = 39 mph =
17.43meters/sec
h= 6ft = 1.8288 meter
angle= -10 degrees (this is a negative angle due to nostril position during a sneeze. The booger will not have a lift in the y direction as depicted the the photo to the right.
Velocity in the X direction (Vx)= 17.43*cos(-10)= 17.17
Velocity in the Y direction (Vy)= 17.43*sin(-10)-9.81*t
Y=1.8288+(17.43455*sin(-10)-9.81t)*t-.5(9.81)*t^2 => Y = 0 at the final X distance
X=17.43*cos(-10)*t => t=X/17.17
Substitute t in to Y equation and solve for X when Y = 0
0=1.8288+(-3.0268(X/17.17)-9.81(X/17.17)^2-.5*9.81(X/17.17)^2
X=4.54meters = 14.9 feet
So after solving for the maximum distance of a sneeze radius, a person can be clear of infection and clear of a booger if they are further than about 15 feet.
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Kinematics!!!
Vo = 39 mph =
17.43meters/sech= 6ft = 1.8288 meter
angle= -10 degrees (this is a negative angle due to nostril position during a sneeze. The booger will not have a lift in the y direction as depicted the the photo to the right.
Velocity in the X direction (Vx)= 17.43*cos(-10)= 17.17
Velocity in the Y direction (Vy)= 17.43*sin(-10)-9.81*t
Y=1.8288+(17.43455*sin(-10)-9.81t)*t-.5(9.81)*t^2 => Y = 0 at the final X distance
X=17.43*cos(-10)*t => t=X/17.17
Substitute t in to Y equation and solve for X when Y = 0
0=1.8288+(-3.0268(X/17.17)-9.81(X/17.17)^2-.5*9.81(X/17.17)^2
X=4.54meters = 14.9 feet
So after solving for the maximum distance of a sneeze radius, a person can be clear of infection and clear of a booger if they are further than about 15 feet.
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