7) A roller coaster moves in different curves as it goes through the bumps in its track. We can easily analyze the forces at any point in the ride, by drawing a circle that matches up with the track at that point
and using our knowledge of centripetal acceleration and centripetal forces. The 550 kg car (with riders)
comes up over the hill at point A and then goes down the hill toward point B, which is 25 m below point A.
10 m
a) What is the fastest that the car can go
over the hill at point A without coming off
the tracks (where the normal force equals 0)?
15 m
B
b) If the car is going 19 m/s (which should be faster than at point a) when it gets to point B, how big is the
normal force provided by the track as the car goes over it at point B?

Aperson walking 1 mile everyday for exercise, leaving her front porch at 9: 00 am and returning to her front porch at 9: 25 am. what is the total displacement of her daily walk? a) 1 mileb) 0c) 25 minutes d) none of the above

Suppose an objects initial velocity is 10m/s and it’s final velocity is 4 m/s. mass is constant. what can best be concluded about the object based in the work-energy theorem

Suppose water is leaking from a tank through a circular hole of area ah at its bottom. when water leaks through a hole, friction and contraction of the stream near the hole reduce the volume of water leaving the tank per second to cah 2gh , where c (0 < c < 1) is an empirical constant. a tank in the form of a right-circular cone standing on end, vertex down, is leaking water through a circular hole in its bottom. (assume the removed apex of the cone is of negligible height and volume.) (a) suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. the differential equation governing the height h in feet of water leaking from a tank after t seconds is dh dt = − 5 6h3/2 . if the height of the water is initially 8 feet, how long will it take the tank to empty? (round your answer to two decimal places.)