Answer:
The car was moving at a speed of approximately 5.240 meters per second along the floor.
Explanation:
Let suppose that the car represents a conservative system, that is, that all non-conservative forces (i.e. friction, air viscosity) can be neglected. The initial speed of the vehicle can be determined by means of the Principle of Energy Conservation, which states that:
[tex]K_{o} = U_{g,f}[/tex] (1)
Where:
[tex]K_{o}[/tex] - Initial translational kinetic energy, measured in joules.
[tex]U_{g,f}[/tex] - Final gravitational potential energy, measured in joules.
By definitions of translational kinetic energy and gravitational potential energy, we expand the equation above:
[tex]\frac{1}{2}\cdot m \cdot v_{o}^{2} = m\cdot g \cdot y_{f}[/tex] (2)
Where:
[tex]m[/tex] - Mass, measured in kilograms.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]v_{o}[/tex] - Initial speed of the car, measured in meters per second.
[tex]y_{f}[/tex] - Final vertical height of the car, measured in meters.
If we know that [tex]m = 0.124\,kg[/tex], [tex]g = 9,807\,\frac{m}{s^{2}}[/tex] and [tex]y_{f} = 1.40\,m[/tex], then the initial speed of the car is:
[tex]v_{o} = \sqrt{2\cdot g \cdot y_{f}}[/tex]
[tex]v_{o} = \sqrt{2\cdot \left(9.807\,\frac{m}{s^{2}} \right)\cdot (1.40\,m)}[/tex]
[tex]v_{o} \approx 5.240\,\frac{m}{s}[/tex]
The car was moving at a speed of approximately 5.240 meters per second along the floor.
