Final answer:
To determine the highest hill a car can coast up (with the engine disengaged), we can use the principle of conservation of mechanical energy. Given that the initial speed of the car is 110 km/h, the car can coast up a hill with a height of 75.2 m.
Step-by-step explanation:
To determine the highest hill a car can coast up (with the engine disengaged), we can use the principle of conservation of mechanical energy.
In this case, the initial kinetic energy of the car is equal to the potential energy it gains while coasting up the hill.
Since work done by friction is negligible, we can assume all the energy is converted to potential energy.
The formula to calculate potential energy is:
PE = mgh
where m is the mass of the car, g is the acceleration due to gravity, and h is the height of the hill.
Given that the initial speed of the car is 110 km/h, we need to convert it to m/s:
110 km/h = 110 imes (1000 m/3600 s) = 30.6 m/s
Using the formula for potential energy, we can plug in the given values:
PE = (750 kg) imes (9.8 m/s^2) imes h = (30.6 m/s)^2 imes (750 kg)
Solving for h:
h = ((30.6 m/s)^2 imes (750 kg)) / (9.8 m/s^2) = 75.2 m
Therefore, the car can coast up a hill with a height of 75.2 m.