I am not as sure but I think it is 9.469 miles
Mechanical energy (ME) is the sum of potential energy (PE) and kinetic energy (KE). When the toy falls, energy is converted from PE to KE, but by conservation of energy, ME (and therefore PE+KE) will remain the same.
Therefore, ME at 0.500 m is the same as ME at 0.830 m (the starting point). It's easier to calculate ME at the starting point because its just PE we need to worry about (but if we wanted to we could calculate the instantaneous PE and KE at 0.500 m too and add them to get the same answer).
At the start:
ME = PE = mgh
ME = 0.900 (9.8) (0.830)
ME = 7.32 J
Answer:
Displacement from the starting position is 103.21m
Explanation:
If you draw these directions, it will create the two legs of a triangle.
Using this method, you can visualize why your displacement is what it is.
Using the pythagorean theorem

Plug in both values


c = 103.2085
c= 103.21
Mechanical waves transfer energy by inducing vibrations in the propagation medium.