A pesky 2.0- m g mosquito is annoying you as you attempt to study physics in you

Question

A pesky 2.0-mg mosquito is annoying you as you attempt to study physics in your room, which is 5.4m wide and 2.5 m high. You decide to swat the bothersome insect as it flies toward you, but you need to estimate its speed to make a successful hit.What is the maximum uncertainty in the horizontal position of the mosquito? (delta x = ? m) What limit does the Heisenberg uncertainty principle place on your ability to know the horizontal velocity of this mosquito? (delta Vx = ? m/s) Is this limitation a serious impediment to your attempt to swat it? (yes/no)

Explanation / Answer

If X is position and P is momentum, then

(deltaX)*(deltaP) >= h/(4pi), where h is planck's constant.

(deltaX)*m(deltaV) >= h/(4pi)

deltaX = 5.4 meters (maximum uncertainty in horizontal position)

(5.4m)*(2.0X10^-6 kg)*(deltaV) >= h/(4pi)

Solving for deltaV:

deltaV >= 4.88X10^-30 m/s

This limitation is not a serious impediment to your attempt to swat the mosquito. (no)

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