Answer
given,
Radius of sphere = 6.38 × 10⁶ m
time = 1 day = 86400 s
[tex]\omega = \dfrac{2\pi}{T}[/tex]
[tex]\omega = \dfrac{2\pi}{ 86400 }[/tex]
[tex]\omega = 7.272 \times 10^{-5}\ rad/s[/tex]
a) at equator
[tex]v = R_E \omega[/tex]
[tex]v = 6.38 \times 10^6\times 7.272 \times 10^{-5}[/tex]
v = 464 m/s
acceleration of the person
[tex]a = \omega^2R_E[/tex]
[tex]a = (7.272 \times 10^{-5})^2(6.38 \times 10^6)[/tex]
[tex]a = 0.03374 m/s^2[/tex]
b) at a latitude of 61.0 ° north of the equator.
[tex]R = R_E cos \theta[/tex]
[tex]R = 6.38 \times 10^6\times cos 61^0[/tex]
[tex]R = 3.093 \times 10^6 m[/tex]
[tex]v = R \omega[/tex]
[tex]v = 3.093 \times 10^6 \times 7.272 \times 10^{-5}[/tex]
[tex]v = 225 m/s[/tex]
acceleration of the person
[tex]a = \omega^2R_E[/tex]
[tex]a = (7.272 \times 10^{-5})^2(3.093 \times 10^6 )[/tex]
[tex]a = 0.01635 m/s^2[/tex]