Final answer:
To find the speed of the tire at the top of the next hill, use the principle of conservation of energy. Equate the initial potential energy to the final kinetic energy using the equations mgh and 0.5mv^2. Solve for v to find the speed of the tire at the top of the next hill. We get approximately 19.8 m/s.
Step-by-step explanation:
To find the speed of the tire at the top of the next hill, we can use the principle of conservation of energy.
Since there is no friction or rotation to consider, we can equate the gravitational potential energy at the first hill with the kinetic energy at the second hill.
The initial potential energy of the tire at the first hill is given by mgh, where m is the mass of the tire (10.0 kg), g is the acceleration due to gravity (9.8 m/s^2), and h is the height of the hill (20.0 m).
So the initial potential energy is 10.0 kg * 9.8 m/s^2 * 20.0 m = 1960 J.
The final kinetic energy of the tire at the second hill is given by 0.5mv^2, where v is the speed of the tire at the top of the hill. So we can solve for v using the equation 0.5 * 10.0 kg * v^2 = 1960 J.
Rearranging the equation, we get
v^2 = 2 * (1960 J / 10.0 kg)
= 392 m^2/s^2.
Taking the square root of both sides, we find that
v = sqrt(392) m/s
≈ 19.8 m/s.
Therefore, the speed of the tire at the top of the next hill is approximately 19.8 m/s.