Solving Momentum & Force for Car & Truck Collision

[faiziqb12]

i have two bodies and their momentum is same ...
say i have a truck and a car and they collide ...
the velocity of car is five times the velocity of truck...
and the mass of the truck is five times the mass of the car...
so my question is how to mathametically prove that the force of the car on the truck will be equal to the force of the truck on the car...


actually i have to find that the time in which the car comes in halt is equal to the time in which the truck comes to halt...

so , please help me with the problem in classic text above , then my problem is solved....
i am using the equation f_ct * t_c = f_tc * t_t
where t_c and t_t is the time in which the car and truck come to halt respectively

and if u have any other method of soving my actual question please post!

thanks in advance

 

[BvU]

Well, the time they are in contact is the same for both, right? So t_c = t_t and there you are ! You have proven Newton's third law

 

[faiziqb12]

thanks

 

[haruspex]

Well, the time they are in contact is the same for both, right? So t_c = t_t and there you are ! You have proven Newton's third law

Not quite that simple.
Since the collision takes time, one or both vehicles must be deformed. So what is meant by a vehicle coming to a halt? The only reasonable interpretation I can think of is to consider the mass centre of the vehicle (though that is changing in relation to the architecture of the vehicle as the deformation occurs).
We can model this as point masses with massless imperfectly elastic springs attached, colliding spring to spring. How will you prove that each mass comes to rest, momentarily at least, at the same instant?