Answer:
292796435 seconds ≈ 300 million seconds
Step-by-step explanation:
First of all, the speed of the car is 121km/h = 33.6111 m/s
The radius of the planet is given to be 7380 km = 7380000 m
From the relationship between linear velocity and angular velocity i.e., v=rw, the angular velocity of the car will be w=v/r = 33.6111/7380000 = 0.000000455 rad/s = 4.55 x 10⁻⁶ rad/sec
If the angular velocity of the vehicle about the planet's center is 9.78 times as large as the angular velocity of the planet then we have
w(vehicle) = 9.78 x w(planet)
w(planet) = w(vehicle)/9.78 = 4.55 x 10⁻⁶ / 9.78 = 4.66 x 10⁻⁷ rad/sec
To find the period of the planet's rotation; we use the equation
w(planet) = 2π÷T
Where w(planet) is the angular velocity of the planet and T is the period
From the equation T = 2π÷w = 2×(22/7) ÷ 4.66 x 10⁻⁷ = 292796435 seconds
Therefore the period of the planet's motion is 292796435 seconds which is approximately 300, 000, 000 (300 million) seconds