What punishment is cruel and unusual? That it is public? That they are executed? Cruel and unusual would be drawing and quartering, or flaying alive, etc. Injecting someone with a sedative and something that stops the heart is not cruel. Heck, people are increasingly being euthanized, so that can't be cruel and unusual.
If you really do care knowing, your answers can be found by reviewing the details of Furman v. Georgia (1972) and Lockett v. Ohio (1978) for relevant Supreme Court precedent.
What punishment is cruel and unusual? That it is public? That they are executed? Cruel and unusual would be drawing and quartering, or flaying alive, etc. Injecting someone with a sedative and something that stops the heart is not cruel. Heck, people are increasingly being euthanized, so that can't be cruel and unusual.
If you really do care knowing, your answers can be found by reviewing the details of Furman v. Georgia (1972) and Lockett v. Ohio (1978) for relevant Supreme Court precedent.