Final answer:
The car will roll for a distance of approximately 16.565 meters before coming to a stop on the hill.
Step-by-step explanation:
The car is initially moving at a speed of 18.2 m/s. When the car starts to coast up the hill, it will gradually lose its kinetic energy due to the upward slope. In this case, since there is no friction involved, the kinetic energy will convert into potential energy as the car gains height.
To calculate the distance the car rolls before coming to a stop, we can use the Conservation of Energy principle. The initial kinetic energy can be converted to potential energy using the equation:
KE_initial = PE_final
1/2 * m * v^2 = m * g * h
Where:
- m is the mass of the car
- v is the initial velocity
- g is the acceleration due to gravity
- h is the height gained
Plugging in the given values, the equation becomes:
1/2 * m * (18.2)^2 = m * 9.8 * h
Cancelling out the m's and solving for h:
h = (1/2 * (18.2)^2) / (9.8)
h = 16.565 m
Therefore, the car will roll for a distance of approximately 16.565 meters before coming to a stop on the hill.