A castle sits at the top of a 100 m tall hill sloping downward to the left. The slope of the hill is 30 ° with respect to the horizontal. What is the minimum velocity for an object to be fired down the hill to just reach the bottom?

Question

anonymous · Answer

I think you're trying to find the initial velocity (vi) and that the final velocity (vf) would be 0 if its hitting the ground at the bottom? If it hits the ground, it ends at rest, so the velocity would drop to 0. Time (t) is not given in the question, but they give you the height of the hill, so I think that would be your y. An equation without t involved could possibly be (vf)^2 = (vi)^2 - 2g(∆x). You're not given ∆x, so using a right triangle, with the 30° angle at the top of the hill, 90° for the right angle at the bottom right, which leaves 60° at the bottom left. Using the law of sines to find the length of x, I found 58m, with a hypotenuse of length 116.

Substituting in the values that you do know:
(0m/s)^2 = (vi)^2 - 2(9.8m/s^2)(58m) = 33.71646482 ≈ 34 m/s.

Does this seem about right?

anonymous · Answer

attachment

primeralph · Answer

fired from the top of the hill?

primeralph · Answer

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anonymous · Answer

Oh, I didn't think about it like that :/ I guess I can't assume that it would be a triangle without the castle involved above it.

primeralph · Answer

yeah,  it depends on the height of the hill.
Either way, you still get a triangle, just that it goes from the top of the castle

primeralph · Answer

..........if that's where the stuff is thrown from

anonymous · Answer

That's all the information I've been given for this question :/ I'm not sure if I can assume that vf would be 0, but I have no idea what variable I can solve for. I feel like I'm missing too many variables to start.

primeralph · Answer

yeah, you're missing the distance of the base from the castle's downward projection or the height of the slope and/or where exactly the stuff is projected from.

anonymous · Answer

Yeah, I don't know what to do. But thanks for checking my question out anyways. (:

primeralph · Answer

you can make an inequality though.............

anonymous · Answer

How so?

primeralph · Answer

take the vertical height of the slope from 0 to a height k where the velocity is minimized.