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Hi Serenity. Not many details here, are there?

Since you say this question has to do with vectors, I suspect there's more to the question than what you've given. I wonder if it's in two parts, perhaps the first part being how long it takes to fall and the second part being how far it goes during the fall? Anyway, let's do the "how long" part.

The equation of motion you want looks like this:

x = (1/2)(a)(t^2) + (v_o)(t)

where (t^2) means "t squared" and (v_o) means the original velocity. X is the distance traveled and t is the time. A is acceleration, which for a body falling freely is the acceleration due to gravity, or g = 9.8 (m/s^2)

What your vector analysis allows you to do here is to separate the vertical motion from the horizontal motion. That means that no matter how fast the car was going horizontally when it went over the cliff, it will still hit the ground below in the same amount of time. Everything here is in the vertical direction, so what is the original vertical velocity?

(SPOILER: the original vertical velocity was 0 -- the car wasn't falling until it went off the cliff.)

Now we substitute in all the stuff we know:

73m = (1/2) (9.8m/s^2)(t^2) + (0)(t)

we have one unknown, the "t" term. Solve for it to find how long it takes for the car to hit.

(SPOILER: I get 3.9s to 2 significant figures.)

So... where is there a 73m cliff we can try this out? :D