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in the last video I realized that I made a mistake near the end but it's not a good one because I copied down the wrong number and then that led to the rest of the problem not having the right values we figured out that the vertical component of our velocity earlier in the video is negative twenty six point zero three meters per second but then I somehow something happened in my brain and it became negative twenty nine point zero three so this is not negative twenty nine point zero three this is negative twenty six point zero three meters per second so the total velocity we should have twenty six point zero three squared over here and then if we evaluate that and I just did it on my calculator twenty six point zero three squared plus five point six one actually I did it wrong again so it's five point two one let me let me redo it so twenty six twenty six point zero three squared plus five point two one squared under the radical gives us twenty six point five five so this right over here should be twenty six point five five meters per second so that is that is the magnitude that is the magnitude of our final velocity so that is the magnitude of our total final velocity and the angle since this is not twenty nine point zero three this is twenty six point zero three we can say that the tangent of this angle theta tangent of theta is equal to just the the raw set this is this value right over here so width is equal to the this the length of this vector right over here which is the opposite side twenty six point zero three over the length of this vector here which is five point two one or we could say we could say if we take the inverse tangent of both sides of this that the angle is equal to the inverse tangent or the arc tangent of twenty six point zero three over five point two one and that gives us we have the inverse tangent of twenty six point zero three divided by five point two 1 gives us seventy eight point roughly seventy eight point seven degrees so the angle here is 78 point seven degrees only eight point seven degrees and it's below the horizontal so we can say we can say that the vector the final velocity vector has a magnitude of twenty six point five five meters per second at a direction of seventy eight point seven degrees below the horizontal so hope I didn't confuse you too much with that mistake at the end of that video