Answer:
a)
Speed at Equator = 463.97 meters per second
Centripetal Acceleration at Equator = [tex]3.37*10^{-2}[/tex] meters per second squared
b)
Speed at 30 degrees north of equator = 401.79 meters per second
Centripetal Acceleration at 30 degrees north of equator = [tex]2.92*10^{-2}[/tex] meters per second squared
Step-by-step explanation:
The formula is:
[tex]v=\frac{2 \pi R}{T}[/tex]
Where
v is speed
R is radius
T is time
and another formula for centripetal acceleration:
[tex]a_c=\frac{4 \pi^{2} R}{T^2}[/tex]
Now,
a)
at equator, the radius is radius of earth (given), time in seconds is
T = 24 * 60 * 60 = 86,400
THus,
[tex]v_E=\frac{2 \pi (6.38*10^{6}}{86,400}=463.97[/tex]
Speed at Equator = 463.97 meters per second
Centripetal Acceleration:
[tex]a_{cE}=\frac{v_E^2}{R_E}=\frac{463.97}{6.38*10^{6}}=3.37*10^{-2}[/tex]
Centripetal Acceleration at Equator = [tex]3.37*10^{-2}[/tex] meters per second squared
b)
At 30.0° north of the equator:
[tex]R_N=R_E Cos (30)= (6.38*10^6)Cos(30)=5.53*10^6[/tex]
Now,
Speed = [tex]v_{30N}=\frac{2 \pi (5.53*10^6)}{86,400}=401.79[/tex]
Speed at 30 degrees north of equator = 401.79 meters per second
Centripetal Acceleration:
[tex]a_{30N}=\frac{v_E^2}{R_E}=\frac{401.79}{5.53*10^6}=2.92*10^{-2}[/tex]
Centripetal Acceleration at 30 degrees north of equator = [tex]2.92*10^{-2}[/tex] meters per second squared
