(a) At the top of the hill, the coaster has total energy (potential and kinetic)
E = (1000 kg) g (10 m) + 1/2 (1000 kg) (6 m/s)² = 116,000 J
As it reaches its lowest position, its potential energy is converted to kinetic energy, and some is lost to friction, making its speed v such that
1/2 (1000 kg) v ² = 116,000 J - 1700 J = 114,300 J
===> v ≈ 15.2 m/s
If no energy is lost to friction as the coaster makes its way up the second hill, all of its kinetic energy would be converted to potential energy at the maximum possible height H.
1/2 (1000 kg) (15.2 m/s)² = (1000 kg) g H
===> H ≈ 11.7 m
(b) At the top of the second hill with minimum height h, and with maximum speed 4.6 m/s, the coaster has energy
E = P + K = (1000 kg) g h + 1/2 (1000 kg) (4.6 m/s)²
Assuming friction isn't a factor again, the energy here should match the energy at the lowest point in part (a), 114,300 J.
(1000 kg) g h + 1/2 (1000 kg) (4.6 m/s)² = 114,300 J
===> h ≈ 10.6 m