From the Greek meaning 'heavy with wine'
A blog devoted to science and reason
Written after a glass or two of Pinot Noir.

Monday, December 23, 2013

Grandma Got Run Over By A Reindeer

Remember this Christmas song?
Grandma got run over by a reindeer
Walking home from our house Christmas eve
You can say there's no such thing as Santa
But as for me and Grandpa, we believe 
She'd been drinkin' too much egg nog
And we'd begged her not to go
But she'd left her medication
So she stumbled out the door into the snow 
When they found her Christmas mornin'
At the scene of the attack
There were hoof prints on her forehead
And incriminatin' Claus marks on her back

So I got to thinking. What would happen in a collision between a reindeer and an elderly woman.

While the song seems to imply that Grandma may have already been lying drunk in the snow and was then trampled by the reindeer, I’ll assume a more violent interaction. She was walking, and the reindeer, running down the road, hit her from behind.
Typical Diagram Drawn by a Physicist
The physics here involves the conservation of momentum. To simplify the problem, I’ll assume that the collision is like the one between billiard balls, what a physicist calls an elastic collision.

Momentum is the product of an object’s mass and its velocity.
A fundamental principle of the universe is that momentum is conserved; that is, this quantity of motion doesn’t change. It is mathematically expressed like this.
In collisions like ones with billiard balls, the total kinetic energy also is constant.
Let’s suppose this reindeer weighs 400 lbs. and was running at a speed of 45 mph. Let’s also suppose Grandma weighs 110 pounds and was walking at 4 mph.

With a bit of algebra we can find what happens to Grandma. It ain’t pretty. Grandma flies forward with a speed of almost 70 mph.
CREDIT: coolthings
Now about this family that let’s an old woman drink too much and then let’s her trudge all alone through the snow.