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Finding the Maximum Height of a Roller Coaster

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The maximum velocity of a roller coaster depends on the vertical drop from the top of the highest hill to the bottom of that hill. The formula: (see attached), gives the relationship between maximum velocity, V(h) in feet per second, and height, h in feet.

1. Identity the independent variable, dependent variable.(Must use the letter to identify variable).
2. What is the domain of the radical function V? (Must show how you get the domain)
3. What is the maximum velocity V(h) of the roller coaster when the height h is 66 feet? (Specify and explain your answer in words).
4. What is the maximum velocity V(h) of the Roller Coaster when the height h is 70 ft. (Use calculator to approximate your answer to two decimals).
5. What is the height h of the roller coaster, if its maximum velocity V(h) is 42 feet per second? (Specify and explain your answer in words)

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This solution addresses 6 algebra question

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Roller Coaster: Maximum speed, forces.

(See attached file for full problem description)

1. A roller coaster ride at an amusement park lifts a car of mass 700kg to point A at a height of 90 m above the lowest point on the track, as shown above. The car starts from rest at point A, rolls with negligible friction down the incline and follows the track around a loop of radius 20 m. Point B, the highest point on the loop, is at a height of 50m above the lowest point on the track.

a. Indicate on the figure the point P at which the maximum speed of the car is attained.
b. Calculate the value Vmax of this maximum speed.
c. Calculate the speed vb of the car at point B.
d. On the figure below, draw and label vectors to represent the forces acting on the car with it is upside down at point B.
e. Calculate the magnitude of all the forces identified in d.
f. Now suppose that friction is not negligible. How could the loop be modified to maintain the same speed at the top of the loop as found in (b)? Justify your answer.

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