Answer:
They will not stop at same elevation
for v=10m/2 => h=5.1m
for v=20m/2 => h=20.4m
Explanation:
If we neglect the effects of friction in the calculations the energy if the system must be conserved. The car energy can be described as a combination of kinetic energy and potential energy:
The potential energy is due to the gravitational forces and can be describes as:
Where g is the gravitation acceleration, m the mass of the car, and h the elevation. This elevation is a relative quantity and any point of reference will do the work, in this case we will consider the base of the hill as h=0.
The kinetic energy is related to the velocity of the car as:
As the energy must be constant E will be always constant, replacing the expressions for kinetic and potenctial energy:
In the base of the hill we have h=0:
When the car stops moving we have v=0:
This two must be equal:
solving for h:
Lets solve for the two cases:
for v=10m/2 => h=5.1m
for v=20m/2 => h=20.4m
As you can see, when the velocity is the double the height it reaches goes to four times the former one.
