If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content
Current time:0:00Total duration:7:53

Video transcript

in the last video I told you that we would figure out the final velocity of when when this thing land so let's do that I did forgot to do it in the last video so let's figure out the final velocity chol and the horizontal components of that final velocity and then we can reconstruct the total final velocity so the horizontal component is easy because we already know that the horizontal component of its velocity is this value right over here which we this is 30 cosine of 80 degrees and that's not going to change at any point in time so this is going to be this is going to be the horizontal component of the projectiles velocity when it lands but what we need to do is figure out the vertical component of its velocity well one thing we did figure out in the last video we figured out what the time in the air is going to be and we know a way of figuring out our final velocity from an initial velocity given our time in the air we know we know that a change in velocity and we're only dealing at the vertical now we're only dealing with the vertical because the horizontal velocity is not going to change we're going to assume we've assumed that air resistance is negligible so we're only dealing with the vertical component right over here we know that the change in velocity we know that the change in velocity or we could say the horizontal the vertical component of the change in velocity is equal to D is equal to the vertical component of the acceleration the vertical component of the acceleration times time now we know what the change in time is we know it is well I'll just write down times our time and what is what is our change in velocity well our change in velocity is our final our final vertical velocity minus our initial vertical velocity and we know what our initial vertical velocity is we solved for it our initial vertical velocity we figured out was 29.54 meters per second that's 30 sine of 80 degrees 29.54 meters per second so this is going to be minus 29.54 meters per second is equal to our acceleration in the vertical direction is negative because it's it's going to accelerating us downwards negative 9.8 meters per second squared and our time in the air is five point six seven seconds times five point six seven seconds and so we can solve for the vertical component of our final velocity so once again this is the vertical component this isn't their total one so the vertical component let me well I wrote vertical up here so you know this is the vertical component so let's solve for this so if you add 29.54 to both sides you get the vertical component of your final velocity final final well it's this vertical component I didn't kind of mark it up here properly is equal to twenty nine point five four meters per second plus nine point eight plus I should say minus really meters per second minus 9.8 meters per second squared times five point six seven times five point six seven seconds the seconds cancel out with one of these seconds so everything is meters per second and so get the calculator out again we have we have twenty nine point five four minus nine point eight times five point six seven so we get we get our change our final velocity is negative twenty six point zero three elsei so this is negative twenty six point zero three meters per second and you might say wait wait cell what is this negative twenty six point oh three meters per second mean remember and when we're dealing in the vertical dimension positive means up negative means down so it means that we're going twenty six point zero three meters per second downwards downwards right when we land right when we land so what is our total what is our total velocity when we when we fall back to that landing so are the the vertical component of our velocity is negative negative twenty nine point oh six times oh three in the in the downward direction and the horizontal component of our velocity we know hadn't changed the entire time that we figured it out was thirty cosine of degrees so that over here is 30 cosine of 80 degrees I'll get the calculator out to calculate it 30 cosine of 80 degrees which is equal to five point two one so this is five point two one meters-per-second five point two one these are both in meters per second so what is the total velocity well I can do the head to tails so I can shift I can shift this guy over so that it's its tail is at the head of the blue vector so it would look like that the length of this the magnitude of our vertical component is is twenty nine point zero three and then we can just use the Pythagorean theorem to figure out the magnitude of the total velocity upon impact so the length of that we could just use the Pythagorean theorem so the magnitude of our total velocity that's this length right over here the magnitude of our total velocity the magnitude of our total velocity or our total final velocity I guess we can say is going to be equal to well that's let me write it this way the magnitude of our total velocity is going to be equal to square root this is just straight from the Pythagorean theorem of five point two one squared plus twenty nine point O three squared twenty nine point zero three squared and we get it as being we get it as being the second let's see the square root of five point two one five point two one squared plus twenty nine point O three squared gives us twenty nine point four nine meters per second this is equal to twenty nine point four nine meters per second that is the magnitude of our final velocity but we also need to figure out its direction and so we need to figure out this angle and now we're talking about an angle below the horizontal or if you wanted to view it in kind of pure terms it would be a negative angle we could say an angle below the horizontal so what is this angle right over here so if we view it as a positive angle just in the traditional trigonometric way we could say that the what we could we could use any of the trig functions we could even use tangent let's use tangent we could say that the tangent of the angle tangent of the angle is equal to the opposite over the adjacent is equal to twenty nine point zero three over five point two one or that theta is equal to the inverse tangent or the arctangent of 29.0 three over five point two one and that gives us that gives us we take the inverse tangent of twenty nine point zero three divided by five point two one and we get seventy nine point eight degrees but it's going to be seventy nine point eight degrees south or I guess below the horizontal below the horizontal or you could view this as an angle of negative seventy nine point eight degrees above the horizontal either one of those either one of those work but we have what's neat about this is we figured out our final velocity vector the entire vector we know what that entire vector is it is twenty nine it is twenty nine point four nine m/s at at seventy nine point eight degrees below the horizontal