Final answer:
The student is asking to solve for the unknown velocity u using the relativistic velocity addition formula given the observer's velocity v as 0.5c and the resultant velocity u' as c.
Step-by-step explanation:
The student appears to be asking about a process related to relativistic velocity transformations in physics, particularly the conversion of one velocity (u) from the perspective of another moving observer (v) and the resultant velocity (u'). To solve for the unknown velocity u when the observer's velocity v is 0.500 times the speed of light (c) and the resultant velocity u' is the speed of light (c), one would need to use the relativistic velocity addition formula:
u = \frac{u' + v}{1 + \frac{uv}{c^2}}
By plugging the known values into this formula, we can find the value of u:
u = \frac{c + 0.500c}{1 + \frac{0.500c \cdot c}{c^2}}
After simplifying the expression, the desired value of u can be calculated.