vectors adding tip to tail — HSC physics year 11, live

Vectors adding tip to tail

A vector has a size and a direction, so adding two of them is a drawing job, not just arithmetic. Place the tail of the second arrow on the tip of the first; the resultant runs from the first tail to the last tip. Its size depends on the angle between them: 4 m/s and 3 m/s give 7 m/s in line, 5 m/s at right angles and 1 m/s head-on. To subtract, reverse the vector and add it: A − B = A + (−B). This is the real knowscape from knowhere, not a picture of one. Drag it. Watch what actually changes.

physics · fundamentals of mechanics · vectors adding tip to taildrag it · it is yours

why this one carries the topic.

Every question here asks one thing: what is the net force? Zero, and motion carries on unchanged. Not zero, and velocity changes. Add that push up over time and you get the momentum change; over distance, the energy change. Split angled forces into components and every problem runs the same way.

Vector A (white) and vector B (amber) sit tip to tail on a grid, and the blue resultant R runs from the start of A to the tip of B, redrawing as you move an arrowhead or turn B to a new angle. Switch to subtract and B flips end for end before it joins, showing A − B = A + (−B).

five things, not forty.

Vectors add tip to tail: the resultant runs from the tail of the first arrow to the tip of the last, and swapping the order gives the same resultant.

The size of a resultant depends on the angle between the vectors, from the full sum when they point the same way down to the difference when they are opposite.

Subtracting a vector means adding its negative: −B has the same length as B but points the opposite way, so A − B = A + (−B).

For perpendicular vectors, find the size of the resultant with Pythagoras and its direction with tan θ = opposite ÷ adjacent, measured from a stated reference.

Velocities in two dimensions combine the same way: a boat's velocity plus the river current gives its velocity relative to the bank, and change in velocity is Δv = v − u.

nothing here is a standalone fact.

knowhere maps every concept to what it rests on and what rests on it — 1 underneath this one, 4 built on top. Each one says why, in a sentence, not as an arrow on a diagram.

this conceptvectors adding tip to tailVector A (white) and vector B (amber) sit tip to tail on a grid, and the blue resultant R runs from the start of A to the tip of B, redrawing as you move an arrowhead or turn B to a new angle.

sits under itdisplacement, velocity and accelerationbecause Knowing that displacement and velocity have a direction as well as a size is what makes them vectors to add.

built on itrelative velocity in two dimensionsbecause vA − vB is built by adding −vB tip to tail, so vector addition must come first.

built on itconnected bodies and rope tensionbecause Forces are vectors: their directions set the signs when you add them.

built on itnewton's laws in everyday situationsbecause Finding the net force means adding force vectors with signs or tip to tail.

built on itcollision lab: momentum before and afterbecause Total momentum is a vector sum; the after arrows add tip to tail, with signs for direction.

10 more, same treatment.

Each one is its own knowscape in the app — built for how a particular student takes things in, not one explanation handed to everybody.

acceleration as a change in velocityin the appmotion graphs of a journeyin the apprelative velocity in two dimensionsin the appconnected bodies and rope tensionin the appstatic and kinetic frictionin the appnewton's laws in everyday situationsin the appblock on a rough inclined planein the appcollision lab: momentum before and afterlive →distance versus displacement, speed versus velocityin the appresolving a vector into componentsin the app

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