King Arthur's knights use a catapult to launch a rock from their vantage point on top of the castle wall, 12 m above the moat. The rock is launched at 25m/s and an angle of 30° above the horizontal. How far from the castle wall does the launched rock hit the ground?
ti=0, xi=0, vi=25, vf=0, a=-9.8
The Attempt at a Solution
So I have a picture drawn of a horizontal line representing the ground/moat, and at one end a vertical line which extends 12m to signify the wall, and then another horizontal line signifying the "above the horizontal" part of the problem, and then a line at a negative slop that is at a 30 degree angle which also connects with the wall/horizontal. I believe I'm visualizing this correctly.
I get that horizontal velocity would be 25cos30. I'm just not quite sure what to do with that information. I sat here and thought about it for a bit and figured that if I used ti=0, xi=0, vi=25, vf=0, a=-9.8, I could use Vf2=Vi2 +2aΔx to find the max height of the rock, and solve it in pieces that way, but that doesn't seem like the best use of the information I'm given, and also sort of defeats the purpose of using angles which is part of the lesson. Any thoughts?