Answer: approximately 34.58 meters for the sled to reach the top
Step-by-step explanation:
To determine the maximum height of the second hump, let's consider the energy conservation principle. The total energy of the sled and rider is conserved as they move along the hill, and this energy is a combination of potential energy and work done against friction.
The initial potential energy at the top of the first hill is converted into potential energy at the top of the second hump and the work done against friction.
The potential energy is given by the formula: PE = m * g * h, where PE is potential energy, m is mass, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height.
1. At the top of the first hill (42 m above the low point), the potential energy is:
PE1 = m * g * 42
2. The work done against friction is given as 3600 J.
3. At the top of the second hump (28 m above the low point), the potential energy is:
PE2 = m * g * 28
According to the conservation of energy, the initial potential energy minus the work done against friction should be equal to the final potential energy:
PE1 - Work = PE2
m * g * 42 - 3600 J = m * g * 28
Now, we can solve for the maximum height (h2) of the second hump:
m * g * 42 - 3600 J = m * g * h2
Substitute values:
50 kg * 9.81 m/s² * 42 m - 3600 J = 50 kg * 9.81 m/s² * h2
Solve for h2:
h2 = (50 * 9.81 * 42 - 3600) / (50 * 9.81)
h2 ≈ (20553 - 3600) / 490.5
h2 ≈ 16953 / 490.5
h2 ≈ 34.58 meters
So, the maximum height of the second hump could be approximately 34.58 meters for the sled to reach the top, assuming the same work in friction and no initial push.