Train Tracks are made of metal. They expand when it is warm and shrink when it is cold. When riding on a train you hear the clickety-clack of the wheels going over small gaps left in the tracks to allow for expansion. Suppose someone lay the track and forgot to put in the gaps so that the track is 1 mile long and firmly fixed at each end. On a hot day, suppose the track expanded by a total of 2 feet and therefore buckled in the middle creating a triangle. How high would the midpoint be?

Aballoon is rising vertically upwards at a velocity of 10m/s. when it is at a height of 45m from the ground, a parachute bails out from it. after 3s he opens his parachute and decelerates ata a constant rate 5m/s.when. (a) what was the height of the parachutist above the ground when he opened his parachute? (b)how far is the parachutist from the balloon at t=3s? (c)with what velocity does the parachutist hit the ground? (d)after how long does the parachutist hit the ground after his exist from the balloon?