A single-celled animal called a paramecium propels itself quite rapidly through water using its hair-like cilia. A certain paramecium experiences a drag force of F d r a g = − b v 2 in water, where the drag coefficient b is approximately 0.290 kg/m . If the paramecium's speed v is 0.000157 m/s , what is the magnitude of the propulsion force that the creature must generate to move at this constant speed?

The magnitude of the propulsion force  is

Explanation:

Given that,

Drag coefficient b= 0.290 kg/m

Speed v = 0.000157 m/s

The drag force is

Since it is given that animal have to generate constant terminal speed.

So if speed becomes constant then we can say its acceleration a = 0

So, The net force is zero.

We need to calculate the magnitude of the propulsion force

Using balance equation

Put the value into the formula

Hence, The magnitude of the propulsion force  is

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