Answer:
a
[tex]v = 7.69 \ m/s [/tex]
b
[tex]a = 19.86 \ m/s^2 [/tex]
Explanation:
From the question we are told that
The radial velocity is [tex]v_r = 4.30 \ m/s[/tex]
The angular velocity is [tex]w = 2.14 \ rad/s[/tex]
The distance considered is [tex]r = 2.98 \ m[/tex]
Converting the angular velocity to its equivalent linear velocity (tangential velocity ) we have that
[tex]v_t = r * w[/tex]
=> [tex]v_t = 2.98 * 2.14 [/tex]
=> [tex]v_t = 6.38 \ m/s [/tex]
Generally the radial and the tangential velocity are perpendicular to each other and their resultant velocity is mathematically represented as
[tex]v = \sqrt{v_r^2 + v_t^2}[/tex]
=> [tex]v = \sqrt{ 4.30^2 + 6.38^2}[/tex]
=> [tex]v = 7.69 \ m/s [/tex]
Generally the acceleration is mathematically represented as
[tex]a = \frac{v^2}{r}[/tex]
=> [tex]a = \frac{7.69^2}{2.98}[/tex]
=> [tex]a = 19.86 \ m/s^2 [/tex]
