Two cars are driving along the road. Car A is traveling at the
speed limit, which is 70 km/h, and is driving in the left lane. Car
B is traveling at 100 km/h in the right lane, looking to pass
Car A. The two cars are the same make and model.
The instant that both cars are level with each other, a tree
falls onto the road. Both drivers react at the same time and apply
the same, constant braking force. Car A is able to stop just before
hitting the tree (right about touching the tree). Obviously, Car B
will hit the tree then. At what speed does Car B crash into the
tree?
Assumptions: The two cars are identical aside from their speed
and paint color. Both drivers react at the same time to the tree.
Braking forces are constant and equal for both cars. Aerodynamic
drag is ignored.