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The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance d apart on the same axle. From the angular displacement Δθ of the two bullet holes in the disks and the rotational speed of the disks, we can determine the speed v of the bullet. Find the bullet speed for the following data: d = 70 cm, ω = 850 rev/min, and Δθ = 31.0°

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Answer:

115.32125 m/s

Explanation:

Distance = 70 cm

Angular speed

[tex]\omega=850\ rpm\\\Rightarrow \omega=850\times \dfrac{360}{60}\\\Rightarrow \omega=5100\ ^{\circ}/s[/tex]

Angular displacement

[tex]\Delta\theta=31^{\circ}[/tex]

Time taken will be

[tex]T=\dfrac{\Delta\theta}{\omega}\\\Rightarrow T=\dfrac{31}{5100}\\\Rightarrow T=0.00607\ s[/tex]

Speed of the bullet would be

[tex]v=\dfrac{Distance}{Time}\\\Rightarrow v=\dfrac{0.7}{0.00607}\\\Rightarrow v=115.32125\ m/s[/tex]

The speed of the bulletis 115.32125 m/s

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