Questions about the amount of force needed to propel 50 pounds 20 feet

[Jhp45]

Ok,
Admittedly, I'm not a physics guy and the question I have is probably pretty simple. However, I don't know the answer and need some expert assistance. Long story short is that my dog was struck by a vehicle last night and I believe the person was traveling well above the posted speed limit. He'll fine and the lady did stop to say she was sorry.

Question: What is the formula for determining the speed of the impacting vehicle?
Any information, as 'dumbed down' (laymans terms) as you can make it, would be VERY helpful for me.

The dog is roughly 24 inches high at the shoulder and roughly 50 pounds and was in motion at the time of being struck. The drag/skid marks from the DOG (not the car- ABS breaks and all) is roughly 20 feet or 7 long strides for me. There's also a positive (uphill) slope involved, but very minimal.

Thank you...

Mike

 

[mfb]

Without details about the physics of the dog (elasticity, friction on the ground and details about the braking process) or tests (...), you won't get a number for the velocity.

 

[Jhp45]

how can one determine the physics of the dog relative to this equation? what factors would need to be used? Braking process would assume a hard stop given there are no skid marks but roughly 40 feet from impact.

 

[Mark M]

Welcome to PF!

As mfb said, there aren't enough details. To calculate the velocity in a simple example you would need to know the friction with the ground, the weight of her car, etc.

 

[Jhp45]

Thanks, Mark M... And mfb... That's why I was hoping someone might have a formula so I can "plug in the numbers" once obtained.

 

[rollcast]

Thanks, Mark M... And mfb... That's why I was hoping someone might have a formula so I can "plug in the numbers" once obtained.

Without knowing a lot more about the variables involved anything said here will be guesswork, as even the difference that would be made if the dog was thrown through the air at angle x or angle y could be massive.

 

[Jhp45]

Understood... But all that can be determined based on a reconstruction of the event itself. Angle would be determined by the height of the cars nose at impact versus the height of the dog and where on the dog the impact occured... Slope of the nose would also be a factor... but, the underlying question still remains, doesn't it? (Forgive my less than mathmatical mind) Is there a formula that says speed of impacting vehicle = angle of subject at impact relative to distance in air and sliding on the ground... I'm sure there are multiple steps needed in factoring a 'realtively close' answer given that this can't be 100% recreated in a test environment. Make sense or do I sound like I'm grasping at straws?

 

[mfb]

You can run a 3-dimensional (or maybe 2-dimensional) reconstruction, but in this case you need all those missing variables: Shape of the car and the dog, the way the dog (and, to a lesser extent, the car) are elastic and so on.

A flight itself is quite easy to calculate: With the horizontal velocity v_x and the vertical velocity v_y, neglecting air resistance, the finite size of the dog and the height difference between car impact and the impact on the street,
the flight distance is $v_x v_y\frac{2}{g}$.

 

[sophiecentaur]

The only clue about the speed of the car would be the length of skid marks. If there are none then it is likely that either the car wasn't going very fast or the driver was so dozy that they didn't react as normal.

This sort of question is very common on PF and the questioner is never given a satisfactory answer, I'm afraid. Perhaps you could look for CCTV coverage of the accident. In all the police series on TV, there seem to be CCTV sequences of everything, from local shops and police cameras.