← Collision calculations in one and two dimensions

Which way after a two-dimensional collision

At an icy intersection, a car sliding east and a car sliding north hit and lock together. Drivers argue afterward about which way the wreck went. Momentum already answers them.

The last lesson's bookkeeping holds here: the system keeps its eastward total and its northward total through the collision. The wreck's direction has to honor both books at once.

Before the impact, the eastbound car carries all the eastward momentum and the northbound car carries all the northward momentum.

seen from above; east is rightward, north is up the pageeastbound carnorthbound careastbound car's momentumnorthbound car's momentum
Before: one car carries the eastward momentum, the other the northward momentum.

After the impact, the locked pair is the whole system. It must still carry the unchanged eastward total and the unchanged northward total.

A wreck sliding due east would carry zero northward momentum, and the northward books would not balance. A wreck sliding due north would abandon the eastward books.

Testing candidate directions for the wreckcandidate directioneastward booksnorthward booksdue eastbalancedo not balancedue northdo not balancebalancebetween east and northbalancebalance
Only a direction between the originals lets both directions' books balance.

So the pair moves off between the two original directions, carrying both totals at once.

Where between? The bigger momentum tilts the direction toward itself. A pair with a large eastward total and a small northward total moves mostly east, tilted a little north.

seen from above; east is rightward, north is up the pageeastbound vannorthbound carlarge eastward momentumsmall northward momentum
Unequal totals: the pair still moves between east and north, now closer to east, the bigger momentum's side.

Equal totals sit in the middle: a pair carrying equal eastward and northward momenta moves off midway between east and north.

This reasoning needs no arithmetic. Two conserved totals, one shared final direction: between the originals, closer to the bigger momentum.

A truck sliding west and a car sliding south collide at an icy intersection and lock together. Predict the rough direction the pair moves off in.

The pair must keep the system's westward total and its southward total.

Due west would abandon the southward books, and due south would abandon the westward books.

So the pair moves off between west and south.

The locked pair moves off between west and south.

At an icy intersection, the eastbound car's momentum is much larger than the northbound car's. The two lock together. Predict the rough direction of the wreck.

The pair moves between east and north, carrying both totals.

The bigger momentum tilts the direction toward itself, and the eastward total is the big one.

The wreck moves off between east and north, closer to east.

A car sliding east and a car sliding north collide at an icy intersection and lock together. In which direction does the pair move off?

At an icy intersection, the eastbound van's momentum is much larger than the northbound car's. They lock together. Which description fits the pair's direction?

Oriana says: 'Two cars with equal-size momenta, one eastward and one northward, lock together, so the pair moves off midway between east and north.' Is she correct?

Your turn

A truck sliding west and a car sliding north collide at an icy intersection and lock together. In which direction does the pair move off?

At an icy intersection, a northbound bus carries far more momentum than an eastbound car. They lock together. Which description fits the pair's direction?

Why must a right-angle sticking collision send the locked pair off BETWEEN the two original directions?