Question

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?

Answer 1

Complete Question

The diagram of with this question is shown on the first uploaded image

Answer:

The value is  $v = -6.543 \^ i + 9.47 \^ j + 0 \^ k$

Explanation:

From the question we are told that

   The mass of the rock is  $m = 0.250 \ kg$

    The length of the string is  $L = 0.75 \ m$

    The angle the string makes horizontal is  $\theta = 11.9^o$

     The angle which the projection of the string onto  the xy -plane makes with the positive x-axis is  $\phi = 34.6^o$

    The angular velocity of the rock is  $w = 2.50 rev/s = 2.50 * 2\pi =15.7 \ rad/s$

Generally the radius of the circle made by the length of the string is mathematically represented as

               $r = L cos(\theta )$

=>            $r = 0.75 cos(11.9 )$

=>            $r = 0.734 \ m$

Generally the resultant tangential velocity is mathematically represented as

      $v__{R}} = w * r$

=>  $v__{R}} = 15.7 *0.734$

=>  $v__{R}} = 11.5 \ m/s$

Generally the tangential velocity along the x-axis is  

      $v_x = -v__{R}} * sin(\phi)$

=>   $v_x =- 11.5 * sin(34.6)$

=>   $v_x = -6.543 \ m/s$

The negative sign show that the velocity is directed toward the negative x-axis

Generally the tangential velocity along the y-axis is  

      $v_y = v__{R}} * cos(\phi)$

=>   $v_y = 11.5 * cos(34.6)$

=>   $v_y = 9.47 \ m/s$

Generally the tangential velocity along the y-axis is  

      $v_z = v__{R}} * cos(90)$

=>   $v_z = 0 \ m/s$

Generally the tangential velocity at that instant is mathematically represented as

       $v = -6.543 \^ i + 9.47 \^ j + 0 \^ k$