Does adding "use strict"; to a function block affect methods and properties added later on to the prototype?

Question

Did a few searches for this and didn't find anything exact. Please consider the following example:

function ConstructIt (param) {
    "use strict";
    // Set up the object
}

My question pertains to each of the following scenarios:

Scenario 1: In the same file as above we have the following code:

ConstructIt.prototype.methodOne = function (fudgeFactor) {
    // Is this still going to be in strict mode due to having it in the constructor above?
    // Or must I include it here as well?
}

OR --> Scenario 2: In a separate file, the same code as Scenario 1 (can come before or after the Constructor, obviously:

ConstructIt.prototype.methodOne = function (fudgeFactor) {
    // Is this still going to be in strict mode due to having it in the constructor above?
    // Or must I include it here as well?
}

In short, what I am trying to understand is how the "use strict"; affects code, and where. Another good question: Why does JShint recommend only using the "function