How long does it take for the pedestrian to reach the front of the vehicle?

[caseys]

This physics problems has me stumped...a vehicle is braking at the time of a collision with a pedestrian. The vehicle is decelerating on a coefficient of friction (cof) of a 0.88. The vehicle and pedestrian reach a common velocity at the windshield of 35 fps. The pedestrian decelerates across the engine hood of the vehicle for a distance of 4 feet on a cof of 0.3

What I am trying to figure out is the amount of time for the pedestrian to exit the front of the vehicle along with the distance that the vehicle traveled during this time.

If the vehicle was not moving the pedestrian would travel 4 feet with a cof of .3 in 0.165 seconds. But with the vehicle moving in the same direction as the pedestrian but with a higher cof of 0.88 this makes the problem more complex.

It is my belief that the time for the pedestrian to travel across the hood would be higher than 0.165 seconds but can not get my brain in gear to figure out the problem.

Any helps or ideas are appreciated.

Casey

 

[Tide]

That's a rather gruesome problem!

I think the way to approach is recognize that the hood is exerting a force on the pedestrian equal to the frictional force (coefficient times weight). Then you just have to account for the motion of the car. I would approximate that the motion of the car is affected very little by the pedestrian. Of course you COULD include that as well (momentum conservation) but you certainly know your requirements better than I do!

 

[LURCH]

I think you must keep in mind that the beginning of the problem, the pedestrian and the vehicle have a common velocity. If you take this velocity as zero, you can then calculate the negative acceleration of the car and determine how long it would take the pedestrian (at that rate of acceleration) to travel 4 feet to the front end of the hood, if the pedestrian and a drag coefficient of zero.

After that, you can factor in the pedestrian's drag coefficient and subtract that from his rate of acceleration towards the nose of the car.