Final answer:
To find the speed of the ride at the 13-meter summit, we apply the conservation of energy principle. Initial mechanical energy (kinetic plus potential) is converted to mechanical energy at the summit, allowing us to calculate the final speed. The ride's mass cancels out in the equation, simplifying the calculation.
Step-by-step explanation:
The scenario described involves the conservation of mechanical energy, where the total mechanical energy (kinetic plus potential energy) of the ride remains constant if we neglect air resistance and friction. Given that the ride starts at a height of 18 meters with an initial speed of 4 m/s, we can find its speed at the top of a 13-meter summit using the principle that the initial total mechanical energy equals the final total mechanical energy.
Initial mechanical energy includes the kinetic energy due to the speed of 4 m/s and the potential energy due to the height of 18 meters. This energy is converted into potential energy at the summit of 13 meters and kinetic energy, which represents the speed at which we want to solve.
Using the conservation of energy formula:
- Kinetic energy initial + Potential energy initial = Kinetic energy final + Potential energy final
- (1/2)mv2 initial + mgh initial = (1/2)mv2 final + mgh final
Assuming the mass m of the ride cancels out from both sides of the equation, we only need to solve for final speed at the 13-meter summit. Plugging in the known values (letting g = 9.81 m/s2):
- (1/2)(4 m/s)2 + (9.81 m/s2)(18 m) = (1/2)v2 final + (9.81 m/s2)(13 m)
We can solve for v final to find out the speed. After rearranging and simplifying, we would get the value of the speed in meters per second (m/s) at the 13-meter summit.