There's a part 61 FAQ that talks a bit about this one. According to it, being under the hood is being in simulated instrument conditions, not "day VFR conditions." But, the FAQ also specifically deals with a situation in which the pilot is under the hood for the whole flight.
My guess is that there is some point where if the pilot is under the hood for too much of the flight, it's not supposed to count. But one instrument approach should be fine. (Especially since, as you read it, you'll see between the lines that it's a revised version of an eralier FAQ that, as I reacll, made it seem that you couldn't do =any= hood time).
Here's the FAQ:
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QUESTION: Could you meet the requirements of § 61.129(a)(3)(iii) and (iv) with a VFR trip in which your instructor placed you under the hood? The regulation specifically calls for day VFR conditions (let's assume for this question that the entire trip was under VFR conditions), so, does the fact that you may be under the hood negate the intent of the regulations?
I guess another way to put it would be to say, the FARs require you to log the conditions of flight. Under 61.51(b)(3), if you log hood time, are you excluded from logging day or night as a condition of the flight?
ANSWER: Ref. § 61.129(a)(3)(iii) and (iv); No, you cannot meet the requirements of § 61.129(a)(3)(iii) and (iv) when the instructor places a hood on the student for the entire cross-country flight and the student never looks outside the aircraft. That kind of flight is instrument flight time under simulated IFR conditions. The intended conditions of these cross-country flights are ". . . VFR conditions . . ." The use of pilotage and/or dead reckoning navigation is the intended cross-country training in § 61.129(a)(3)(iii) and (iv).
You indicated in your question that the ". . . instructor placed you under the hood . . ." and I am assume what you are saying is the instructor placed the student under the hood for the entire cross-country flight. So the question you are asking and the question I am answering is a cross-country training flight where the instructor placed the student under the hood for the entire cross-country flight. Otherwise, the student never looked outside the aircraft during the entire cross-country flight except for the takeoff and landing phase of the cross-country flight. So, essentially, the flight was instrument flight time. The student did not perform pilotage or dead reckoning navigation. The student navigated by the use of radio aids. The student was wearing a hood/view limiting device for the entire cross-country flight.
Per § 61.129(a)(3)(iii), it states:
(iii) One cross-country flight of at least 2 hours in a single-engine airplane in day VFR conditions, consisting of a total straight-line distance of more than 100 nautical miles from the original point of departure;
VFR stands for visual flight rules.
Per § 61.129(a)(3)(iv), it states:
(iv) One cross-country flight of at least 2 hours in a single-engine airplane in night VFR conditions, consisting of a total straight-line distance of more than 100 nautical miles from the original point of departure; and
And again, VFR stands for visual flight rules.
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