Final answer:
To solve the equation uₜₜ = c²uₓₓ for 0, we can use the equation u = v/u'. Plugging in the known values, we find that u = -2/3c.
Step-by-step explanation:
To solve the equation uₜₜ = c²uₓₓ for 0, we can start by identifying the knowns and unknowns. The knowns are v = 0.500c and u' = -0.750c. The unknown is u. The appropriate equation to use is u = v/u'. Plugging in the known values, we get u = 0.500c/(-0.750c). Simplifying this expression, we find that u = -2/3c.