Alice's friends Bob and Charlie are having a race to a distant star 10 light years away. Alice is the race official who stays on Earth, and her friend Darien is stationed on the star where the race ends. Bob is in a rocket that can travel at 0.7c; whereas Charlie's rocket can reach a speed of 0.866c. Bob and Charlie start at the same time. Draw space- diagrams from each perspective. Required:
Estimate how long it takes Bob and Charlie to finish the race from each perspective.

Solution :

The distance between the starting point and the end point, = 10 light years

But due to the relativistic motion of Bob and Charlie, the distance will be reduced following the Lorentz contraction. The contracted length will be different since they are moving with different speeds.

For Bob,

Speed of Bob's rocket with respect to Alice,

So the distance appeared to Bob due to the length contraction,

Therefore, the time required to finish the race by Bob is

  = 10.143 year

For Charlie,

Speed of Charlie's rocket with respect to Alice,

So the distance appeared to Charlie due to the length contraction,

The time required to finish the race by Charlie is

  = 5.77 year

the word that best describes martin luther king jr.'s tone in the video is dignified

martin luther king, jr. was a social activist and baptist minister who played a key role in the american civil rights movement from the mid-1950s until his assassination in 1968. the video shows his manner and attitude having or showing a composed or serious manner that is worthy of respect so dignified is the correct answer

kepler used the data from tycho blahe (his mentor) to construct the laws of planetary motion.