Answer:
1800seconds
Explanation:
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Answer:
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Explanation: North Korea and Cuba are the only places you can't buy Coca-Cola
A girl swings a 0.250 kg rock attached to a taut string in a circle around her head. Her hand holds the end of the string above her head, and the string angles down slightly (11.9° below the horizontal.). The string is massless and 0.75m long.
A coordinate system lies with its origin a the location where the string comes out of the girl's hand. The positive z-axis points vertically. the projection onto the horizontal plane is such that the string makes an angle of 34.6° with the x-axis.
At a certain instant, the rock makes 2.50 revolutions per second (rev/s) in a counterclockwise direction as seen from above.
What is the tangential velocity vector at this instant?
Complete Question
The diagram of with this question is shown on the first uploaded image
Answer:
The value is [tex]v = -6.543 \^ i + 9.47 \^ j + 0 \^ k[/tex]
Explanation:
From the question we are told that
The mass of the rock is [tex]m = 0.250 \ kg[/tex]
The length of the string is [tex]L = 0.75 \ m[/tex]
The angle the string makes horizontal is [tex]\theta = 11.9^o[/tex]
The angle which the projection of the string onto the xy -plane makes with the positive x-axis is [tex]\phi = 34.6^o[/tex]
The angular velocity of the rock is [tex]w = 2.50 rev/s = 2.50 * 2\pi =15.7 \ rad/s[/tex]
Generally the radius of the circle made by the length of the string is mathematically represented as
[tex]r = L cos(\theta )[/tex]
=> [tex]r = 0.75 cos(11.9 )[/tex]
=> [tex]r = 0.734 \ m[/tex]
Generally the resultant tangential velocity is mathematically represented as
[tex]v__{R}} = w * r[/tex]
=> [tex]v__{R}} = 15.7 *0.734[/tex]
=> [tex]v__{R}} = 11.5 \ m/s[/tex]
Generally the tangential velocity along the x-axis is
[tex]v_x = -v__{R}} * sin(\phi)[/tex]
=> [tex]v_x =- 11.5 * sin(34.6)[/tex]
=> [tex]v_x = -6.543 \ m/s[/tex]
The negative sign show that the velocity is directed toward the negative x-axis
Generally the tangential velocity along the y-axis is
[tex]v_y = v__{R}} * cos(\phi)[/tex]
=> [tex]v_y = 11.5 * cos(34.6)[/tex]
=> [tex]v_y = 9.47 \ m/s[/tex]
Generally the tangential velocity along the y-axis is
[tex]v_z = v__{R}} * cos(90)[/tex]
=> [tex]v_z = 0 \ m/s[/tex]
Generally the tangential velocity at that instant is mathematically represented as
[tex]v = -6.543 \^ i + 9.47 \^ j + 0 \^ k[/tex]