A futuristic train rushes past you at an incredible, relativistic speed such that it appears to only be 80% as long as you know it to be. At what speed is that train traveling from the point of view of your reference frame

v = 0.6c = 1.8 x 10⁸ m/s

Explanation:

From Einstein's theory of relativity, we know that the length of an object contracts while traveling at a speed relative to speed of light. The contraction is according to following equation:

where,

L = Relative Length

L₀ = Rest Length

According to given:

L = 0.8 L₀

c = speed of light = 3 x 10⁸ m/s

v = relative speed of train = ?

Therefore,

squaring on both sides:

taking square root on both sides:

v = 0.6c = 1.8 x 10⁸ m/s

C. 28.2 deg

Explanation:

The horizontal range of a projectile is given as:

where,

R = Range

v = speed

θ = angle of launch

g = acceleration due to gravity = 9.81 m/s²

First, we will find the launch speed (v) by using the initial conditions:

R = 120 m

θ = 45°

Therefore,

Now, consider the second scenario to hit the target:

R = 100 m

Therefore,

Hence, the correct option is:

C. 28.2 deg