Mosquito Horsepower

Classical Mechanics Level 1

An exceptionally fast (and strong) mosquito pushes on the back of a moving airplane.

The mosquito supplies a force of 1 N 1 N and does work on the plane at a rate of 1 h p 1 hp .

At what mach number (multiple of the speed of sound) is the airplane moving?

Assume:
- The speed of sound is 330 m / s 330 m/s
- 1 h p = 746 W 1 hp = 746 W


The answer is 2.2606.

Steven Chase by Steven Chase , 37, USA

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1 solution

Kb E
Nov 23, 2017

P = F ⃗ ⋅ v ⃗ = F v P = \vec{F}\cdot \vec{v} = Fv as the mosquito supplies the force in the same direction as the plane’s velocity. Then, P = 746 W = 1 N ⋅ v ⟹ v = 746 m / s P= 746 W = 1 N \cdot v \implies v = 746 m/s . Therefore the mach number of the plane is 746 330 = 2.206 \frac{746}{330} = 2.206 .

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