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Suppose a car manufacturer tested its cars for front-end collisions by hauling them up on a crane and dropping them from a certain height. height corresponds to a collision at 60 km/h ?

Respuesta :

Answer:

[tex]H = 14.2 m[/tex]

Explanation:

  • Neglecting air friction, The kinetic energy at the ground equals the potential energy at height H relative to the ground. This is conservation of mechanical energy.

So

        [tex]\frac{1}{2}m v^2=mgH[/tex]

             [tex]\frac{v^2}{2}=gH[/tex]

In terms of H:  

                 [tex]H = \frac{v^2}{2 g}[/tex]

[tex]60 km/h[/tex] equals [tex](60/3.6) m/s = 16.7 m/s.[/tex]

Thus the corresponding height is

[tex]H = (16.7 m/s)^2/(2*9.81 m/s^2) = 14.2 m[/tex]

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