Final answer:
The car will coast for approximately 5.588 meters before starting to roll back down the slope.
Step-by-step explanation:
To find the distance the car will coast before starting to roll back down, we need to consider the forces acting on it. The car is traveling up a 9.0° slope, which means that the component of gravity pulling it back down the slope is less than the component of gravity pulling it in the direction of the slope. Therefore, the car will coast for a certain distance before it starts rolling back down. To calculate this distance, we need to find the horizontal component of the car's velocity.
The horizontal component of the car's velocity is given by v_horizontal = v * cos(θ), where v is the car's velocity and θ is the angle of the slope. Substituting the given values, we have v_horizontal = 24 m/s * cos(9.0°). Calculating this, we get v_horizontal ≈ 23.39 m/s. Now, we can calculate the distance the car will coast before starting to roll back down using the formula d = (v_horizontal^2) / (2 * g), where d is the distance, v_horizontal is the horizontal component of the velocity, and g is the acceleration due to gravity. Substituting the values, we have d = (23.39 m/s)^2 / (2 * 9.8 m/s^2). Calculating this, we get d ≈ 5.588 m. Therefore, the car will coast for approximately 5.588 meters before starting to roll back down.