Answer:
a)
Speed at Equator = 463.97 meters per second
Centripetal Acceleration at Equator =
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 =
meters per second squared
Step-by-step explanation:
The formula is:
![v=\frac{2 \pi R}{T}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B2%20%5Cpi%20R%7D%7BT%7D)
Where
v is speed
R is radius
T is time
and another formula for centripetal acceleration:
![a_c=\frac{4 \pi^{2} R}{T^2}](https://tex.z-dn.net/?f=a_c%3D%5Cfrac%7B4%20%5Cpi%5E%7B2%7D%20R%7D%7BT%5E2%7D)
Now,
a)
at equator, the radius is radius of earth (given), time in seconds is
T = 24 * 60 * 60 = 86,400
THus,
![v_E=\frac{2 \pi (6.38*10^{6}}{86,400}=463.97](https://tex.z-dn.net/?f=v_E%3D%5Cfrac%7B2%20%5Cpi%20%286.38%2A10%5E%7B6%7D%7D%7B86%2C400%7D%3D463.97)
Speed at Equator = 463.97 meters per second
Centripetal Acceleration:
![a_{cE}=\frac{v_E^2}{R_E}=\frac{463.97}{6.38*10^{6}}=3.37*10^{-2}](https://tex.z-dn.net/?f=a_%7BcE%7D%3D%5Cfrac%7Bv_E%5E2%7D%7BR_E%7D%3D%5Cfrac%7B463.97%7D%7B6.38%2A10%5E%7B6%7D%7D%3D3.37%2A10%5E%7B-2%7D)
Centripetal Acceleration at Equator =
meters per second squared
b)
At 30.0° north of the equator:
![R_N=R_E Cos (30)= (6.38*10^6)Cos(30)=5.53*10^6](https://tex.z-dn.net/?f=R_N%3DR_E%20Cos%20%2830%29%3D%20%286.38%2A10%5E6%29Cos%2830%29%3D5.53%2A10%5E6)
Now,
Speed = ![v_{30N}=\frac{2 \pi (5.53*10^6)}{86,400}=401.79](https://tex.z-dn.net/?f=v_%7B30N%7D%3D%5Cfrac%7B2%20%5Cpi%20%285.53%2A10%5E6%29%7D%7B86%2C400%7D%3D401.79)
Speed at 30 degrees north of equator = 401.79 meters per second
Centripetal Acceleration:
![a_{30N}=\frac{v_E^2}{R_E}=\frac{401.79}{5.53*10^6}=2.92*10^{-2}](https://tex.z-dn.net/?f=a_%7B30N%7D%3D%5Cfrac%7Bv_E%5E2%7D%7BR_E%7D%3D%5Cfrac%7B401.79%7D%7B5.53%2A10%5E6%7D%3D2.92%2A10%5E%7B-2%7D)
Centripetal Acceleration at 30 degrees north of equator =
meters per second squared