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Consider a railroad bridge over a highway. A train passing over the bridge dislodges a loose bolt from the bridge, which proceeds to fall straight down and ends up breaking the windshield of a car passing under the bridge. The car was 39 m away from the point of impact when the bolt began to fall down; unfortunately, the driver did not notice it and proceeded at constant speed of 19 m/s. How high is the bridge? Or more precisely, how high are the railroad tracks above the windshield height? The acceleration due to gravity is 9.8 m/s 2 .

Respuesta :

Answer:

The railroad is 20,63 m height.

Explanation:

In this problem we have two objects that encounter on a given time that is the same for both objects.

Objects are:

  • The car
  • the bolt.

The car moves in constant velocity of 19 m/s. The car makes a trajectory of 39 mts before encounter the bolt that hits the windshield.

Then, for the car we need to find the time that takes to make the trajectory, and we use the formula for  uniform rectilinear motion (URM):

[tex]v=\frac{s}{t}[/tex]

where v is velocity, s is space or trajectory, and t is time.

[tex]t=\frac{s}{v} =\frac{39}{19} \\t=2.052 sec[/tex]

The time t=2.052 sec is the time that takes the bolt to fall and hit the windshield, so, we have to take this time and replace it in following formula that applies for free fall objects:

[tex]h=\frac{1}{2}*g*t^{2} \\h=\frac{1}{2}*9.8*2.052^{2} \\h=20.63 m[/tex]

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