Question

Piloting X-wings is dangerous. An overly sharp turn can kill a pilot due to the intense acceleration that their body can be subject to. While flying to the mysterious planet Exegol, Rey had to navigate a treacherous route through space. Some of her turns were very tight, with radius of curvature as little as 1.4 km. What is the maximum speed Rey could safely attain while keeping acceleration on her body below 6 g's? (recall that the letter 'g' here stands for the Earth's surface gravity g=9.8 m/s^2

Answer 1

The maximum velocity is
`v= 287 m/s`

Step-by-step explanation:

From the question we are told that

The radius of curvature is
`r = 1.4 \ km`

The acceleration of the body is
`a = 6 g = 6 * 9.8 = 58.8 \ m/s^2`

Generally the centripetal acceleration of this body is mathematically represented as

`a_c = (v^2)/(r)`

and from the question we are told that
`a_c \le (6g = 58.8 m/s^2)`

Which implies that

`58.8 = (v^2)/(r)`

Substituting values

`58.8 = (v^2)/(1400)`

=>
`v= √(58.8 * 1400)`

`v= 287 m/s`

Answer 2

the maximum speed Rey could safely attain while keeping acceleration on her body below 6 g's is 91.65 m/s

Step-by-step explanation:

Using the approach of Centripetal acceleration:

`a=( V^2)/(R)`

Given that:

acceleration on her body below 6 g

(i.e a < 6g)

`6 = (V^2)/(R)`

where;

R = radius of curvature = 1.4 km = 1400 m

`V^2 = 6*1400`

`V^2 = 8400`

`V = √(8400)`

V = 91.65 m/s

Thus; the maximum speed Rey could safely attain while keeping acceleration on her body below 6 g's is 91.65 m/s