I'll bet you're trying to get us to do your homework for you, but this
question has enough interesting features beyond the standard homework
answer that it's worth talking about.
You haven't specified the mass of the car, but it's not that
relevant (as long as it's much more than that of the motorcycle and
driver). The total momentum of the system points along the road, with
only a small sidways component as the motorcyclist changes his lanes.
So the momentum after the collision should point down the road, and
that's the general direction both the car and the motorcycle should be
going after the collision. But, collisions can be complicated, and
there are lots of things that could happen:
1) The motorcycle can just bounce off of the car. More likely, the
motorcycle will dent the car, lose its momentum transverse to the
direction along the road, and move with the car, but not be stuck to
it, after the collision. The motorcyclist should try to steer back into
his lane if at all possible at this point, eventually slow down, and
negotiate with the car's driver whose insurance is going to pay for the
dent. Lane changes are usually very slow (sideways velocity components
are usually less than 1 mph) so this outcome is actually not too
unlikely, but some other scenarios may happen instead:
2) As in 1, the motorcycle bounces off of the car, but loses
control. This can happen especially if the part of the motorcycle which
makes contact with the car is the handlebar or the front tire. If the
front wheel gets turned to the side, it will yank the motorcycle
violently in that direction. Which direction that is depends on the
details of the collision.
It is not a good idea to turn a motorcycle's front wheel while
going 45 MPH down a road -- the motorcycle could flip over, tossing the
motorcycle rider at the car or in the other direction, neither of which
sounds good, especially since the motorcycle driver is wearing light
clothes (always a bad idea when riding a motorcycle). The motorcycle
driver could be struck by his motorcycle, abraded by the road, or even
run over by the car, or perhaps all three. Because of strong frictional
forces with the road (and with the car, especially if it is the
rotating tire making contact with the car body or tire), the
conservation of momentum argument made in 1) won't apply and bad things
can happen. I once saw two motorcycles going down a high-speed
expressway, one trailing the other by inches. The front tire of the
back motorcycle made contact with the rear tire of the leading
motorcycle; the rear motorcycle flipped over backwards, throwing the
riders.
3) Only in James Bond and similar movies -- the car could have a
latching mechanism which can pick up the motorcycle and carry it away.
This would be in our mechanics class a "totally inelastic collision".
By the way, if a motorcycle attempts to ride up into the back of a
truck by means of a ramp extended from the truck, while going at 45 MPH
down a road (they probably do this in James Bond movies), this will
almost certainly involve an accident, as the rotation speed of the
wheels has to be very different when in contact with the ground and
when in contact with the ramp of the moving truck.
Tom
(published on 10/22/2007)
