## Monday, January 27, 2020

### Calculate the velocity of the vehicle

 Hat tip to C.W. Swanson for the image

I might have a chance to do some pro bono physics tutoring.

Bella solved the problem by inspection. "At the end of the clip the velocity is approximately zero."

Then she challenged me to solve for the velocity in meters/second at the start of the clip.

Approximations:
The gap is slightly longer than the vehicle as the vehicle goes airborn. Let's approximate the gap as 20 feet wide or about six meters.

The front of the vehicle impacts the moving face approximately two feet below the roadbed. The point of impact on the vehicle is approximately 24 inches above the bottoms of the tires. Total drop is 48" or 1.2 meters.

X)t=X)0 +V)0*t +0.5*A)0*t^2
Set coordinate system so X)0 and V)0 are zero.

X)t=A)g*t^2

t^2=X)t/A)g=1.2/9.8=1.2
t=sqrt(1.22)= 1.1 seconds

Velocity is the distance divided by the time. 6m/1.1s = 5.4m/s
In US units that is about 12mph

Looking at the superficial damage to the hood and fenders, 12mph is a plausible impact velocity.