Question

A roller coaster starts with the cars being pulled up a ramp. The mass of the cars is estimated by the function m(p) = 175p + 1,180 where p is the number of passengers in the car. The potential energy of the car is calculated using the function E(m) = 9.8mh, 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 1

Answer:

$E(p)=51,450p+346,920$

Step-by-step explanation:

The function

$m(p) = 175p + 1,180$

gives the mass of the car as a function of the number of passengers in it.

And the function

$E(m) = 9.8m*h$

gives the potential energy of the car as a function of the car's mass.

Now if the height of the ramp is 30 meters, we have

$E(m) =9.8m*(30)$

$E(m) =294m$

And to find the potential energy as a function of the number of passengers, we just substitute $m(p)$ into $E(m)$ to get:

$E(m(p))=294(175p+1180)$

$\boxed{ E(p)=51,450p+346,920}$

which gives the potential energy as a function of the number of passengers.