Final answer:
The speed at which the jet rocket must travel around Earth's equator just above its surface in order to have a magnitude of acceleration equal to g is approximately 7.9 km/s.
Step-by-step explanation:
To find the speed at which the jet rocket must travel, we need to use the formula for centripetal acceleration. The magnitude of the acceleration is equal to the acceleration due to gravity, which is g. The centripetal acceleration can be calculated using the formula a = v^2 / r, where v is the speed and r is the radius of the circular path. Since the jet rocket is traveling along the equator just above the surface, its radius will be equal to the radius of the Earth.
The radius of the Earth is approximately 6,371 km. Plugging this value into the centripetal acceleration formula, we have g = v^2 / 6,371 km. Rearranging the equation to solve for v, we get v = √(6,371 km * g).
Using the value of g as 9.8 m/s² (the acceleration due to gravity on Earth), we can calculate the speed:
v = √(6,371 km * 9.8 m/s²) ≈ 7.9 km/s (rounded to one decimal place).
Therefore, the correct answer is a) 7.8 km/s.