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American eels (Anguilla rostrata) are freshwater fish with long, slender bodies that we can treat as uniform cylinders1.0mlong and 10cm in diameter. An eel compensates for its small jaw and teeth by holding onto prey with its mouth and then rapidly spinning its body around its long axis to tear off a piece of flesh. Eels have been recorded to spin at up to 14 revolutions per second when feeding in this way. Although this feeding method is costly in terms of energy, it allows the eel to feed on larger prey than it otherwise could

A field researcher uses the slow-motion feature on her phone’s camera to shoot a video of an eel spinning at its maximum rate. The camera records at 120 frames per second. Through what angle does the eel rotate from one frame to the next?

1. ${\mathbf{1}}^{\mathbf{∘}}$
   
2. ${\mathbf{10}}^{\mathbf{∘}}$
   
3. ${\mathbf{22}}^{\mathbf{∘}}$
   
4. ${\mathbf{42}}^{\mathbf{∘}}$

Step by step solution

01

The relationship between angle and revolution

The relationship between angle and revolution is given by,

$\mathit{θ}\mathbf{=}\mathit{n}\mathbf{â‹\dots }{\mathbf{360}}^{\mathbf{∘}}$ (1)

where n is the number of revolution.

02

Identification of given data

Here ell make 14 revolution. So,$n=14$

Also, the number of photos camera takes In one second is$N=120$

03

Finding angle the eel rotate from one frame to the next

By equation (1) we have,

$\mathrm{θ}=nâ‹\dots {360}^{∘}$

We have,$n=14$

$\begin{array}{l}⇒\mathrm{θ}=\left(14\right)â‹\dots {360}^{∘}\\ ⇒\mathrm{θ}={5040}^{∘}\end{array}$

Now, based on the total angle the ell describes during 1 second and the number of photographs the camera makes each second.

We can find the angle by which the ell moves between consecutive photographers.

Let the angle by which the ell moves between consecutive photographers is $\mathrm{δ}$.

$\begin{array}{l}⇒\mathrm{δ}=\frac{\mathrm{θ}}{N}\\ ⇒\mathrm{δ}=\frac{{5040}^{∘}}{120}\\ ⇒\mathrm{δ}={42}^{∘}\end{array}$

Hence, the angle by which the ell moves between consecutive photographers is$\mathrm{δ}={42}^{∘}$

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