Question

A spaceship is traveling at a speed of 0.398c? What is "gamma"?

A spaceship is traveling at a speed of 0.99989c? What is "gamma"?​

How fast, in terms of c, must you be going for "gamma" to equal 2.1?​

How fast, in terms of c, must you be going for "gamma" to equal 79.000?​

Answer 1

v = speed of the spaceship = 0.398 c

gamma is given as

= 1/sqrt(1 - (v/c)²)

inserting the values

= 1/sqrt(1 - (0.398 c/c)²)

= 1/sqrt(1 - (0.398)²)

= 1.090054

v = speed of the spaceship = 0.99989 c

gamma is given as

= 1/sqrt(1 - (v/c)²)

inserting the values

= 1/sqrt(1 - (0.99989 c/c)²)

= 1/sqrt(1 - (0.99989)²)

= 67.4

given that : = 2.1

1/sqrt(1 - (v/c)²) = 2.1

sqrt(1 - (v/c)²) = 1/2.1

(1 - (v/c)²) = (1/2.1)²

(v/c)² = 1 - (1/2.1)²

v = c sqrt(1 - (1/2.1)²)

v = 0.88 c

given that : = 79

1/sqrt(1 - (v/c)²) = 79

sqrt(1 - (v/c)²) = 1/79

(1 - (v/c)²) = (1/79)²

(v/c)² = 1 - (1/79)²

v = c sqrt(1 - (1/79)²)

v = 0.9999 c