You are driving along an empty country road at night. The speed limit for going around bends is 90km/hr and you have been keeping to the speed limits. As you come out of a bend onto a straight road...

You are driving along an empty country road at night. The speed limit for going around bends is 90km/hr and you have been keeping to the speed limits. As you come out of a bend onto a straight road you change from low to high beam and see what looks to be a white tree blocking the road 55m in front of you! You slam on the brakes which slows you down at a constant 5.60m/s2. Just as you are about to hit the tree it vanishes and you realise it was an effect produced by the reflection of light off mist across the road.
a) It feels like forever but how long did it take you to cover the distance between when you first notices the "tree" and when it vanished?
b) If there had been a tree there, with what speed would you have crashed in to it?
Problem 2 Children's adventure stories sometimes have a path that leads to a secret cave hidden behind a waterfall. Let us pretend that in one particular story it is possible to lead your fully laden donkey along the path between the falling water and the sheer rock face, to get to the cave behind the waterfall. This can all be done without you, the donkey or the goods on the donkey getting wet.
a)Estimate the speed of the water flowing over the edge of the cliff if the top of the sheer rock face is 5m above the path.
b) You are asked to build a movie set that could be used for filming the scene but the producers want to make the waterfall larger, however they cannot give you the exact details of how much larger yet. So that you are ready when they are ready find the