. (a) How high a hill can a car coast up (engine disengaged) if work done by friction is negligible

and its initial speed is 110 km/h? (b) If, in actuality, a 750-kg car with an initial speed of 110 km/h
is observed to coast up a hill to a height 22.0 m above its starting point, how much thermal energy
was generated by friction? (c) What is the average force of friction if the hill has a slope 2.5°
above the horizontal?

a. V=110km/h = 110000m/3600s.=30.56 m/s

V^2 = Vo^2 + 2g*h
h = (V^2-Vo^2)/2g = (0-(30.56)^2/-19.6 =
47.6 m.

To answer these questions, we need to understand the concepts of work, energy, and friction. Let's take each question one by one and explain how to approach them.

(a) How high a hill can a car coast up (engine disengaged) if work done by friction is negligible and its initial speed is 110 km/h?

To determine the maximum height the car can coast up, we need to consider the conservation of mechanical energy. When the engine is disengaged, the only external force acting on the car is gravity. Therefore, at the highest point of the hill, all of the car's initial kinetic energy will be converted into gravitational potential energy.

We need to find the height of the hill using the formula for gravitational potential energy:

mgh = 1/2 mv^2

where m is the mass of the car, g is the acceleration due to gravity, h is the height of the hill, and v is the initial speed of the car. Rearranging the equation to solve for h:

h = (1/2)v^2 / g

Substituting the given values:

v = 110 km/h = (110 * 1000) m/3600 s = 305.6 m/s
g = 9.8 m/s^2

Plugging in these values, we can calculate the height h.

(b) If, in actuality, a 750-kg car with an initial speed of 110 km/h is observed to coast up a hill to a height 22.0 m above its starting point, how much thermal energy was generated by friction?

To determine the thermal energy generated by friction, we need to consider the difference between the mechanical energy gained (height achieved) and the initial mechanical energy (initial kinetic energy). This difference is equal to the work done by friction.

The initial kinetic energy is given by:

KE_initial = 1/2 mv^2

where m is the mass of the car and v is the initial speed. Substituting the given values:

m = 750 kg
v = 110 km/h = (110 * 1000) m/3600 s = 305.6 m/s

The mechanical energy gained (height achieved) is equal to the gravitational potential energy at the top of the hill and is given by:

PE_gained = mgh

where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the hill. Substituting the given values:

m = 750 kg
g = 9.8 m/s^2
h = 22.0 m

The thermal energy generated can be calculated as the difference:

Thermal Energy = PE_gained - KE_initial

(c) What is the average force of friction if the hill has a slope 2.5° above the horizontal?

To determine the average force of friction, we need to consider the component of gravitational force acting parallel to the slope of the hill. This force is equal in magnitude to the force of friction.

The gravitational force acting on the car can be calculated using the formula:

F_gravity = mg

where m is the mass of the car and g is the acceleration due to gravity.

The component of gravitational force acting parallel to the slope can be found using trigonometry:

F_parallel = F_gravity * sin(θ)

where θ is the angle of the slope.

Since the average force of friction is equal in magnitude to F_parallel, we can calculate it using the equation above.