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]
