A friend in a spaceship travels past you at a high speed. He tells you that his ship is 20m long and that the identical ship you are sitting in is 19m long. According to your observations,
(a) how long is your ship??
(B) how long is his ship??
(c) what is the speed of your friend's ship??
Please help i really don't understand this.
a) 20 m
b) according to you: 19 m
Solve for the speed using the Lorentz contraction formula:
19 = 20/gamma = 20 sqrt[1-v^2/c^2]
a=19 b=20
c=100000000000000000000000
To solve for the speed of your friend's ship, we need to rearrange the Lorentz contraction formula to isolate the speed (v). Here's how we can do it step by step:
Step 1: Start with the equation:
19 = 20/γ = 20√[1-v^2/c^2]
Step 2: Square both sides of the equation to eliminate the square root:
19^2 = (20/γ)^2 = 400/(γ^2) = 400/(1-v^2/c^2)
Step 3: Multiply both sides of the equation by (1-v^2/c^2) to eliminate the denominator:
(1-v^2/c^2) * 19^2 = 400
Step 4: Expand the left side of the equation:
19^2 - 19^2 * v^2/c^2 = 400
Step 5: Simplify the equation:
V^2 * 19^2/c^2 = 19^2 - 400
Step 6: Divide both sides of the equation by 19^2 to isolate v^2/c^2:
v^2/c^2 = (19^2 - 400) / 19^2
Step 7: Take the square root of both sides to find v:
v/c = √[(19^2 - 400)/19^2]
Step 8: Simplify the equation:
v/c = √[(361 - 400)/361]
v/c = √(-39/361) [Note: the negative sign indicates that the relative velocity is in the opposite direction]
Step 9: Calculate the square root:
v/c = -0.165
Step 10: Multiply both sides of the equation by c to find v:
v = -0.165 * c
Therefore, the speed of your friend's ship is approximately -0.165 times the speed of light (c).
It's worth noting that this answer implies that your friend's ship is traveling in the opposite direction from you. If you're looking for the magnitude of the speed (i.e., ignoring direction), you can take the absolute value of the result (0.165c).