If 7.00hp are required to drive a 1500-kg automobile at 66.0 km/h on a level road. What power is necessary to drive the car at 66.0 km/h down a 1.00 % grade? It requires 42.9 hp to drive the car at 66.0 km/h up a 10.0 % grade (a hill rising 10.0 m vertically in 100.0 m horizontally). The total retarding force due to friction, air resistance, and so on is 285 N

To find the power required to drive the car at 66.0 km/h down a 1.00% grade, we need to consider the forces acting on the car.

1. First, let's calculate the force due to gravity acting on the car as it goes downhill.

The force due to gravity can be calculated using the formula:

Force due to gravity = mass * acceleration due to gravity

Given:
mass of the car = 1500 kg
acceleration due to gravity = 9.8 m/s^2

So, the force due to gravity = 1500 kg * 9.8 m/s^2

2. Next, let's take into account the force of air resistance and friction acting against the car. The total retarding force is given as 285 N.

3. Now, let's calculate the power required to overcome the forces acting against the car.

Power = force * velocity

Since the car is moving at 66.0 km/h, we need to convert it to m/s:

66.0 km/h = 66.0 * (1000 m/3600 s)

Finally, we can calculate the power:

Power = (force due to gravity + total retarding force) * velocity

Substituting the values we have:

Power = (1500 kg * 9.8 m/s^2 + 285 N) * (66.0 * (1000 m/3600 s))

Therefore, the power required to drive the car at 66.0 km/h down a 1.00 % grade can be found using the above equation.

To find the power necessary to drive the car at 66.0 km/h down a 1.00% grade, we need to consider the force acting on the car due to the grade.

Step 1: Convert the speed from km/h to m/s.
Speed in m/s = 66.0 km/h × (1000 m/km) / (60 s/min × 60 min/hr)
Speed in m/s = 18.33 m/s

Step 2: Calculate the force due to the grade.
Force due to grade = mass × gravity × sin(θ)
where,
mass is the mass of the car (1500 kg),
gravity is the acceleration due to gravity (9.8 m/s^2), and
θ is the angle of the grade (1.00%).

θ is given as a percentage, so we need to convert it to radians.
θ (in radians) = θ (in degrees) × (π/180)
θ (in radians) = 1.00% × (π/180)

Force due to grade = 1500 kg × 9.8 m/s^2 × 0.01 × π/180

Step 3: Calculate the power required.
Power (in watts) = Force × velocity
Power (in watts) = (Force due to grade + Total retarding force) × 18.33 m/s

Step 4: Convert power from watts to horsepower.
Power (in horsepower) = Power (in watts) / 745.7

Therefore, the necessary power to drive the car at 66.0 km/h down a 1.00% grade can be found using the above steps.