A mosquito of mass 0.15 mg is found to be flying at a speed of 50 cm/s with an uncertainty of 0.5 mm/s. (a) How precisely may its position be known? (b) Does this inherent uncertainty present any hindrance to the application of classical mechanics?

a) Δx = t 0.05 + 0.5

, Δx = 0.5 cm, b) Do not present any problem

Explanation:

The kinematic equation for constant speed is

v = x / t

x = v t

a) the uncertainty can be calculated with

Δx = dx / dv Δv + dx / dt Δt

Δx = t Δv + v Δt

Speed is

v = (50.00 ± 0.05) cm / s

The most common uncertainty for the time of Δt = 0.01 s

We replace

Δx = t 0.05 + 50 0.01

Δx = t 0.05 + 0.5

We must know the time to have an explicit value, if we assume that the measure was t = 1s

Δx = 0.5 cm

b)

Do not present any problem since its value is not very small, we must take as soon as the quantum effects and the velocity are not so high that we must take into account the relativistic effects