Question

In Newtonian mechanics, velocities add in an intuitive way: so if a launcher that can launch a ball horizontally at 20 m launches a ball forward while on a car moving at 30 m/s, the ball is launched at 50 m/s relative to the ground (you could say u = vtu', where u' is the velocity of object within the reference frame moving relative to the "lab", u is the velocity of the object in the lab frame, and v is the speed of the moving reference frame relative to the lab frame). In special relativity, velocities do not add in an intuitive way, instead, they add according to this formula: +u' 1+ ru' / Try below calculations to help you understand the meaning of this formula. All velocities are given as fraction of speed of light e (so no need to enter e; factors of e cancel out in the formula) Hint Review Section 14.4 Relativistic Addition of Velocities if necessary a. Suppose that a pitcher who can throw a ball at u' = 0.0000001c is on a truck moving at v=0.0000001c. The velocity of the ball relative to the ground as the pitcher throws the ball forward is = (The agreement between this and the results of Newtonian mechanics is called correspondence principle ) b. Suppose that a spaceship fires a relativistic kinetic missile at u' =0.9c relative to itself while approaching its target at v 0.5c. The speed of the relativistic kinetic missile as measured by the target is c c. Suppose the spaceship fires a laser beam at a target (so u' = c, since it's light) while approaching its target at U 0.5e. The speed of the laser beam as measured by the target is u e. (This is consistent with the second postulate of special relativity, as to be expected.)

Answer 1

u= cхlot+cx15 7 I + 2 xicly or ez u= 2xlota (b) u= 0.5C+0.90 A B 1+5x0.92 0-5x0.902 = c2 0.9655 C u= 0. 5c+ o.o 1+0. 5² € - Sac