Question

An experimental jet rocket travels around Earth along its equator just above its surface. At what speed must the jet travel if the magnitude of its acceleration is 1.6g? Assume the Earth's radius is 6.370 x 10⁶ m.

v - __________

Answer 1

To sustain an acceleration of 1.6g while flying along the Earth's equator, the jet must travel at approximately 9950 m/s, calculated using the formula for centripetal acceleration with Earth's given radius.

Step-by-step explanation:

To determine the speed at which the experimental jet rocket must travel along the equator to maintain an acceleration of 1.6g, we use the formula for centripetal acceleration: a = v^2 / r, where a is the centripetal acceleration, v is the tangential velocity, and r is the radius of the circular path (in this case, Earth's radius). Given that 1g is approximately 9.80 m/s², the jet must sustain an acceleration of 1.6 times this value, which is 1.6g = 1.6 x 9.80 m/s² = 15.68 m/s².

Substituting the given values into the formula yields:

v = √(a × r)

Therefore:

v = √(15.68 m/s² × 6.370 x 10⁶ m)

Calculating this gives us the required speed of the experimental jet to be approximately 9.937 x 10⁳ m/s or about 9950 m/s. This is the speed at which the jet must travel to have a centripetal acceleration of 1.6g while flying along the equator just above Earth's surface.