Answer:
The railroad tracks are 13 m above the windshield (12 m without intermediate rounding).
Explanation:
First, let´s calculate the time it took the driver to travel the 27 m to the point of impact.
The equation for the position of the car is:
x = v · t
Where
x = position at time t
v = velocity
t = time
x = v · t
27 m = 17 m/s · t
27 m / 17 m/s = t
t = 1.6 s
Now let´s calculate the distance traveled by the bolt in that time. Let´s place the origin of the frame of reference at the height of the windshield:
The position of the bolt will be:
y = y0 + 1/2 · g · t²
Where
y = height of the bolt at time t
y0 = initial height of the bolt
g = acceleration due to gravity
t = time
Since the origin of the frame of reference is located at the windshield, at time 1.6 s the height of the bolt will be 0 m (impact on the windshield). Then, we can calculate the initial height of the bolt which is the height of the railroad tracks above the windshield:
y = y0 + 1/2 · g · t²
0 = y0 -1/2 · 9.8 m/s² · (1.6 s)²
y0 = 13 m
