Stranding the preposition
When the preposition stays close to the verb as in ‘the food they can’t do without’ we say that i is stranded, that is, displaced from its position in a PC. The verb and the preposition stay together, with the stress usually on the verb. Stranding of prepositions occurs in several constructions, one of which is the relative clause.
Relative clauses have two alternatives, one in which the preposition is fronted to the position before its complement, as in 2a and 2b; the other is stranded, that is, separated from its complement which, as in 3a and 3b in the examples below:
1a We listened to some music. 1b I looked after their cat.
2a The music [to which we listened] 2b *The cat [after which I looked]
3a The music [which we listened to] 3b The cat [which I looked after]
Comparing the behavior of listen +to with that of look + after, we can see that listen +to admits both fronting, as in 2a and stranding, as in 3a. By contrast, look + after admits only stranding, as in 3b. The fronted type, as in 2b, is ungrammatical.
Many prepositional verbs, in particular those of Types 2 and 3, admit both the fronted and the stranded variants. A considerable number of idiomatic prepositional verbs, however, admit only stranding. Type 1 verbs, the most idiomatic, are of this kind.
Verbs of both types are illustrated in the following block:

Although, grammatically, stranding is the marked form, it has become the normal, unmarked form used in conversation. The non-stranded form, when it occurs, is reserved for formal contexts and genres such as academic prose. But even in highly formal situations, the stranded form is usually preferred in the spoken language, both BrE and AmE, as the following quotation illustrates. The speaker is the then US Secretary of State, Colin Powell, addressing the United Nations Council in February 2003:
What we need is not more inspections. What we need is not more immediate access. What we need is immediate full unconditional cooperation by Irak. To this day we have not seen the level of cooperation that was expected, looked for, hoped for.