v =84 km/h= 23.33 m/s.
mv^2/2+mgh = mgH.
H = h +v^2/2g =51 +27.78 =78.78 m.
mv^2/2+mgh = mgH.
H = h +v^2/2g =51 +27.78 =78.78 m.
Here's how we can solve the problem:
1. Convert the speed from km/h to m/s:
Speed = 84 km/h = (84 * 1000 m) / (3600 s) = 23.3 m/s
2. Calculate the initial potential energy at the top of the first hill using the car's mass and height:
Potential Energy at the top of the first hill = mass * gravity * height
Let's assume the mass of the car is 1000 kg and gravity is approximately 9.8 m/s^2:
Potential Energy = 1000 kg * 9.8 m/s^2 * 51 m = 499,800 J (Joules)
3. Calculate the final potential energy at the maximum height the car reaches:
Since there is no friction or drag, the total mechanical energy (kinetic energy + potential energy) is conserved. Therefore, the final potential energy will be equal to the initial potential energy:
Final Potential Energy = 499,800 J
4. Calculate the height of the next hill using the final potential energy:
Final Potential Energy = mass * gravity * height
Rearranging the equation to solve for height:
height = Final Potential Energy / (mass * gravity)
height = 499,800 J / (1000 kg * 9.8 m/s^2) ≈ 51 meters
Therefore, the car will coast up the next hill to a height of approximately 51 meters, the same as the height of the first hill.