How Do You Calculate the Speed of Vehicle B After Impact?

[mhb22079]

It has been years since I have taken physics and for the life of me I cannot figure out how to solve the following real-world problem.

Given 2 vehicles a & b:
a's speed = 0, weight = 4,250 lbs
b's speed = x, weight = 3,260 lbs.

After b impacts a from behind and leaving a space of 8 feet between the two vehicles, what is the is approximate speed of vehicle B. I realize of course road conditions, brakes applied, vehicle absorbing the blow, etc plays a big part but I'm just trying to get a near-figure.

Thanks!

 

[Kurdt]

this is a conservation of momentum question where the initial momentum must be equal to the final momentum. The initial momentum is clearly:

$$p_i = m_b v_bi$$

The momentum immediately after impact must be equivalent to this:

$$p_f = m_a v_a + m_b v_bf = p_i = m_b v_bi$$

The only problem I can see is working out the velocity soon after impact. Is there any other data supplied with this question or not? If not just make an estimate of the deceleration of car a and work backwards from the distance moved.

 

[al_201314]

Apologise for hijacking the thread may I ask something regarding momentum as well.

In my syllabus I'm usually given questions on head-on collisions with masses moving in the same direction intially one faster than another or one being stationary.

Lets say if there are 2 masses moving in the opposite directions approaching each other before collision, for the total KE of the system, should I add or find the difference the KE of the 2 masses? I suppose it is to add as it is in traveling in the same direction since KE is a scalar?

Thanks for the clarification.

 

[deepakalways]

"Lets say if there are 2 masses moving in the opposite directions approaching each other before collision, for the total KE of the system, should I add or find the difference the KE of the 2 masses? I suppose it is to add as it is in traveling in the same direction since KE is a scalar?"

no al 201314, you always add the KEs as its a scalar

 

[Hootenanny]

An important point to note however, is that kinetic energy is only conserved in elastic collisions.