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A particle travels in a straight line with speed v.

The particle slows down and changes direction. The new speed of the particle is v\2

The new velocity has a component of v\4

in the same direction as the initial path of the particle.

Through which angle has the particle turned?

A 27° B 30° C 45° D 60°

Respuesta :

skyluke89

Answer:

D 60°

Explanation:

Using trigonometry:

- The new speed (v/2) of the particle corresponds to the hypothenuse

- The component of v/4 represents the side adjacent  to the angle that we want fo find, [tex]\theta[/tex]

So we can write:

[tex]cos \theta = \frac{adjacent}{hypothenuse}=\frac{v/4}{v/2}=\frac{1}{2}[/tex]

So we find the angle

[tex]\theta= cos^{-1} (\frac{1}{2})=60^{\circ}[/tex]

Answer:

D 60°

Explanation:

Using trigonometry in the attached image:

[tex]cos\alpha =\frac{v/4}{v/2}[/tex]

[tex]cos\alpha =\frac{1}{2}[/tex]

[tex]\alpha =cos^{-1} \frac{1}{2}[/tex]

Angle=60°

Ver imagen miguel9418

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