As Brent's spacecraft overtakes Jasmin's identical spacecraft at high speed, Brent notifies Jasmin that his spacecraft is 39.0 m long; Jasmin's spacecraft appears to be 33.0 m long according to his observations. (a) What is the length of Jasmin's spacecraft in her frame of reference? tions (b) What is the length of Brent's spacecraft as observed by Jasmin? orate Ultra ummary (c) What is the relative speed between their spacecrafts?

a. 39.0 m, b. 33.0m, c. 0.532c

Explanation:

The proper length is the length of an object measured in its rest frame. When the object moves at a velocity comparable to the speed of light, with respect to an observer, then the length of the object appears to be contracted to the observer. The object undergoes maximum length contraction when the length of the object is in the direction of its motion and zero when the length of the object is perpendicular to its direction of motion. The expression for length contraction is given as

L = L'√1 - (v²/c²), consider this to be equation (1), where L is the length of object in the rest frame of observer, L' is the length of object in its own rest frame, v is the velocity of object with respect to observer, and c is the speed of light.

a. Both the space crafts are identical which means that their length in their rest frame is same. This means the rest length of Brent's spacecraft is equal to the rest length of Jasmine's spacecraft. The length of Brent's spacecraft in his own frame is 39.0m since both the space crafts are identical in their rest frames, the length of Jasmine's space craft is equal to the length of the Brent's space craft in her rest frame.

Thus, the length of Jasmine's space craft in her frame of reference is 39.0 m.

b. The relative velocity of Jasmine's spacecraft with respect to the Brent's spacecraft is equal to the relative velocity of the Brent's spacecraft with respect to the Jasmine spacecraft but opposite in direction. The length of Brent's craft as seen from the Jasmine's spacecraft is the same as the length of Jasmine's spacecraft as seen from Brent's spacecraft as they are identical in their rest frames.

Thus, the length of Brent's space craft as seen from Jasmine's space craft is 33.0 m.

c. The length of the spacecraft in its rest frame is the rest length. The length of the space craft of Jasmine observes by Brent is the contracted length.

The expression for length contraction using equation (1) is given as follows

L = L' √1 - (v²/c²)

Rearranging the above expression for v

V = c√[1 - (33/39) ²]

V = 0.532c

Thus, the relative velocity is 0.532c