Answer:
approximately 30.5 meters
Step-by-step explanation:
To find the maximum height y2, you can use the conservation of energy principle. The total initial energy of the roller coaster is the sum of its kinetic energy and potential energy:
Ei = KEi + PEi = 1/2mv0^2 + mgy0
where m is the mass of the roller coaster, v0 is the initial speed, g is the acceleration due to gravity (9.8 m/s^2), and y0 is the initial height.
Since there is no friction, the total energy of the roller coaster is conserved throughout the ride. At the highest point y2, all of the initial energy has been converted to potential energy:
Ef = PEmax = mgy2
where y2 is the maximum height that the roller coaster reaches.
Equating the initial and final energies, we get:
Ei = Ef
1/2mv0^2 + mgy0 = mgy2
Simplifying and solving for y2, we get:
y2 = y0 + v0^2/2g
Plugging in the given values, we get:
y2 = 6 m + (9.4 m/s)^2 / (2 x 9.8 m/s^2)
y2 ≈ 30.5 m
Therefore, the maximum height that the roller coaster will reach is approximately 30.5 meters.