A 10kg roller coaster does a loop-de-loop and it’s your job to make sure it is safe. The people will fall out if the cart’s speed is less than 40m/s when it goes upside down. How high up does the car have to be at point A to make it? Fill in everything else as well. Location

PE

KE

TE

A

h =

v = 0m/s

B

h = 0m

v =

C

h = 15m

PE=m*g*h

v = 40m/s

KE=0.5*m*v2=

TE=PE+KE

D

h = 0m

v =

E

h = 10m

v =

F

h = 20m

v =

An engineer designs a roller coaster so that a car travels horizontally for 152 ft, then climbs 137 ft at an angle of 34.0° above the horizontal. it then moves 137 ft at an angle of 48.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

"an open tank has the shape of a right circular cone. the tank is 6 feet across the top and 5 feet high. how much work is done in emptying the tank by pumping the water over the top edge? note: the density of water is 62.4 lbs per cubic foot."

What is a neurotransmitter involved in mood reward, addiction, and motor behaviors?