This question is incomplete, the complete question is;
The Millennium Falcon is chased by the Imperial Forces. The ship is moving at a speed of 0.525 c. Han Solo is shooting at the imperial fighters with his newly installed proton cannon purchased at the MSU Surplus Store for $20.00 plus 6.00% TAX. The cannon emits protons at a speed of 0.741 c with respect to the ship.
What is the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction? 0.911 ANS .
What is the velocity of the protons in the resting frame when the cannon is shot in the backward direction?
(Use positive sign for the forward direction, and negative for the backward direction.)
Answer:
A)
the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction is 0.911c
B)
the velocity of the protons in the resting frame when the cannon is shot in the backward direction -0.3535c.
The negative sign indicates that the proton is moving in the opposite direction of the ship. (backward)
Step-by-step explanation:
Given that;
speed of ship u = 0.525C
speed of proton emission v = 0.741C
Now When Cannon is shot in Forward Direction
Relativistic speed S is Calculated as;
S = (u+v) / ((1 + (uv))/c²)
we substitute (0.525 + 0.741 )C / ((1 + (0.525 × 0.741) C)/c²)
the C² cancel each other
so we have
S = 1.266 / 1.389925
S = 0.9108 ≈ 0.911c
Therefore the velocity of the protons in the resting frame of the movie audience in terms of the speed of the light when the cannon is shot in the forward direction is 0.911c
When Cannon is shot in Backward Direction
Relativistic speed S is Calculated as;
S = ( u – v ) / ( 1 – uv / c ²)
S = (0.525 - 0.741) C / ((1 - (0.525 × 0.741) C)/c²)
the C² cancel each other
so S = -0.216 / 0.610975
S = -0.3535c
The negative sign indicates that the proton is moving in the opposite direction of the ship. (backward)
Therefore the velocity of the protons in the resting frame when the cannon is shot in the backward direction -0.3535c.
