Answer:
the bridge has a height y₀ = 6.94 m
Step-by-step explanation:
The position y of the loose bolt is given by (0,y) where
y = y₀ - 1/2*g*t²
where
y₀ = initial position of the bolt (height of the bridge) , g= gravity , t=time
and the position x of the car is given by (x,0) where
x= x₀ + v*t
where
x₀= initial position of the car
v= car's velocity
then in order for the bolt to hit the windshield they should be at x=0 and y=0 at the same time , then
0= x₀ + v*t
t= -x₀/v
replacing in the equation for y
0 = y₀ - 1/2*g*t²
0 = y₀ - 1/2*g*(-x₀/v)²
0 = y₀ - 1/2*g*x₀²/v²
y₀ = 1/2*g*x₀²/v²
replacing values
y₀ = 1/2*g*x₀²/v² = 1/2* 9.8m/s² * (-25 m)²/(21 m/s)² = 6.94 m
then the bridge has a height y₀ =6.94 m
We have assumed that
- The bolt has no horizontal velocity ( only vertical velocity) , starts from rest and neglected air friction
- Neglecting the height of the car , position of the windshield and size of the loose bolt