Question

A car is moving along level ground at 25m/s. When it arrives at the base of a hill at 10 degrees, the driver takes his foot off the pedal and coasts up the hill. How far up the hill does the car move? How high above the original surface is the car at this point?

Answer 1

To solve for how far and how high the car will go up the hill, we use the conservation of energy. The initial kinetic energy is set equal to the potential energy gained, which allows us to solve for the height. The distance up the hill is then found using the height and the angle of the incline.

Step-by-step explanation:

To determine how far up the hill a car moves and how high above the original surface it is at that point, we will use the principle of conservation of energy. The initial kinetic energy of the car is converted into potential energy as it coasts up the hill without any work done by friction. The initial kinetic energy (KE) can be calculated using the formula KE = ½ mv², where m is the mass of the car and v is the initial speed.

The potential energy gained at the highest point of the hill (PE) is given by PE = mgh, where g is the acceleration due to gravity, and h is the height above the original surface. If we set the initial kinetic energy equal to the potential energy at the peak of the hill (KE = PE), we get ½ mv² = mgh. We can then solve for h to find the height as h = v² / (2g).

To find out how far the car travels up the slope, we can use the height and the angle of the slope (θ) to determine the distance (d) along the slope using the trigonometric relationship d = h / sin(θ).