Main content

## Two-dimensional projectile motion

# Correction to total final velocity for projectile

## Video transcript

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 26.03
meters per second. But then something
happened in my brain, and it became negative 29.03. So this is not negative 29.03. This is negative 26.03
meters per second. So the total velocity, we should
have 26.03 squared over here. And then if we evaluate
that-- and I just did it on my calculator--
26.03 squared plus 5.61. Actually, I did it wrong again. So it's 5.21. Let me redo it. So 26.03 squared plus 5.21
squared under the radical gives us 26.55. So this right over here should
be 26.55 meters per second. So 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 29.03, this is 26.03, we can say that the tangent
of this angle theta-- this is this value right
over here-- is equal to the length of this
vector right over here, which is the opposite side 26.03
over the length of this vector here, which is 5.21. Or 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 arctangent, of 26.03 over 5.21. We have the inverse
tangent of 26.03 divided by 5.21 gives
us roughly 78.7 degrees. So the angle here
is 78.7 degrees. And it's below the horizontal. So we can say that the vector,
the final velocity vector, has a magnitude of
26.55 meters per second at a direction of 78.7
degrees below the horizontal. So I hope I didn't
confuse you too much with that mistake
at the end of that video.