A roller coaster starts with the cars being pulled up a ramp. The mass of the cars is estimated by the function m times p is equal to 175 p plus 1 comma 180 where p is the number of passengers in the car. The potential energy of the car is calculated using the function cap e times m is equal to 9 point 8 m h , where h is the height of the ramp. If the top of the ramp is 30 meters, which function can be used to calculate the potential energy of a car in terms of the number of passengers?
Answer
A
open paren cap e times open paren m times p close paren close paren is equal to 294 p plus 1 comma 180
B
open paren cap e times open paren m times p close paren close paren is equal to 51 comma 450 p plus 1 comma 180
C
open paren cap e times open paren m times p close paren close paren is equal to 1 comma 715 p plus 1 comma 180
D
open paren cap e times open paren m times p close paren close paren is equal to 51 comma 450 p plus 346 comma 920
Explanation
The car’s mass with p passengers is m(p) = 175p + 1,180. At a height of 30 meters, potential energy is E(m) = 9.8m(30) = 294m. Substitute the mass function: E(m(p)) = 294(175p + 1,180) = 51,450p + 346,920, which is choice C.
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