how fast would you have to be traveling at in a spaceship in order to appear to age 20% slower than your classmate left behind on earth
sqrt[1 -(v/c)^2] = 0.8
1 - (v/c)^2 = 0.64
(v/c)^2 = 0.36
v = 0.6 c
60% of the speed of light would be required.
Sorry can you explain how you get 0.64? Square rooting both sides? sqrt of 0.8 is 0.89 on the calculator. Please help.
Nevermind lol.. you squared it.
Nevermind lol.. you squared it.
To calculate the speed required for time dilation, we can refer to the theory of relativity. According to the theory, time dilation occurs when an object moves at a high velocity relative to another object.
The formula to calculate time dilation due to relative velocity is as follows:
t' = t * sqrt(1 - (v^2/c^2))
Where:
t' is the dilated time experienced by the moving object
t is the proper time of the stationary object (in this case, the classmate on Earth)
v is the relative velocity between the two objects
c is the speed of light in a vacuum (~3 x 10^8 meters per second)
In this scenario, we want the dilated time (t') to be 20% slower than the proper time (t). Mathematically, that can be expressed as:
t' = t - 0.2t = 0.8t
Now, we need to solve the equation:
0.8t = t * sqrt(1 - (v^2/c^2))
Let's simplify this equation:
0.8 = sqrt(1 - (v^2/c^2))
Square both sides to eliminate the square root:
0.64 = 1 - (v^2/c^2)
Rearrange the equation:
(v^2/c^2) = 1 - 0.64 = 0.36
Now, solve for v^2:
v^2 = 0.36 * c^2
v = sqrt(0.36) * c
v ≈ 0.6 * c
Therefore, to appear to age 20% slower than your classmate left behind on Earth, you would need to travel at approximately 0.6 times the speed of light.