Answer:
[tex]\mathbf{V_x = 3.25 \ cm/s}[/tex]
[tex]\mathbf{V_y = 1.29\ cm/s}[/tex]
Explanation:
Given that:
The radius of the table r = 16 cm = 0.16 m
The angular velocity = 45 rpm
= [tex]45 \times \dfrac{1}{60}(2 \pi)[/tex]
= 4.71 rad/s
However, the relative velocity of the bug with turntable is:
v = 3.5 cm/s = 0.035 m/s
Thus, the time taken to reach the bug to the end is:
[tex]t = \dfrac{r}{v}[/tex]
[tex]t = \dfrac{0.16}{0.035}[/tex]
t = 4.571s
So the angle made by the radius r with the horizontal during the time the bug gets to the end is:
[tex]\theta = \omega t[/tex]
[tex]\theta = 4.712 \times 4.571[/tex]
[tex]\theta = 21.54^0[/tex]
Now, the velocity components of the bug with respect to the table is:
[tex]V_x = Vcos \theta[/tex]
[tex]V_x = 0.035 \times cos (21.54^0)[/tex]
[tex]V_x = 0.0325 \ m/s[/tex]
[tex]\text {V_x = 3.25 \ cm/s}[/tex][tex]\mathbf{V_x = 3.25 \ cm/s}[/tex]
Also, for the vertical component of the velocity [tex]V_y[/tex]
[tex]V_y = V sin \theta[/tex]
[tex]V_y = 0.035 \times sin (21.54^0)[/tex]
[tex]V_y = 0.0129\ m/s[/tex]
[tex]\mathbf{V_y = 1.29\ cm/s}[/tex]
