# Velocity after a totally inelastic collision

## Homework Statement

You are driving your 1000-kg car at a velocity of(25 m/s )ι^ when a 9.0-g bug splatters on your windshield. Before the collision, the bug was traveling at a velocity of (-1.5 m/s )ι^.
What is the change in velocity of the car due to its encounter with the bug?

## Homework Equations

pi = pf
m1v1 + m2v2 = (m1 + m2)v

## The Attempt at a Solution

p1 + p2 = (m1 + m2)v
(2.5 x 10^4) + (-1.35 x 10^-2) = (1000 + 0.009)v
v = 25 m/s

Chestermiller
Mentor
So is there a question here?

So is there a question here?
Yes. The question is "What is the change in velocity of the car due to its encounter with the bug?". I also came up with an answer but it was incorrect.

Chestermiller
Mentor
Yes. The question is "What is the change in velocity of the car due to its encounter with the bug?". I also came up with an answer but it was incorrect.
You got the correct equation for the final velocity, and I am just going to re-write it out for you as follows:

$$v=\frac{(2.5 \times 10^4-1.35 \times 10^{-2})}{1000+0.009}$$

If you subtract the original velocity of the car, you get the change in velocity Δv:

$$Δv=\frac{(2.5 \times 10^4-1.35 \times 10^{-2})}{1000+0.009}-25$$

Now, what I would like you to do is to reduce the relationship to a common denominator, without first evaluating the first term and without combining terms in the numerator. What do you get?

Chet