Final answer:
To find the speed of the car at the top of the hill, we can use the principle of conservation of energy. The speed is approximately 14 m/s.
Step-by-step explanation:
To find the speed of the car at the top of the hill, we can use the principle of conservation of energy. At the top of the starting hill, the car has gravitational potential energy. As it goes down the slope, this potential energy is converted into kinetic energy. The car reaches its maximum kinetic energy at the bottom of the slope. Then, as it climbs the hill, it loses kinetic energy and gains potential energy.
Since there is no friction, the total mechanical energy of the car is conserved. So we can equate the initial potential energy at the starting hill to the final potential energy at the top of the hill. The equation is: m * g * h1 = m * g * h2 + (1/2) * m * v^2, where m is the mass of the car, g is the acceleration due to gravity, h1 is the starting elevation, h2 is the elevation at the top of the hill, and v is the velocity of the car at the top of the hill.
Substituting the given values, we have (mass cancels out): 9.8 * 26 = 9.8 * 16 + (1/2) * v^2. Solving for v, we get v ≈ 14 m/s. Therefore, the speed of the car at the top of the hill is approximately 14 m/s.