What Was the Initial Velocity of the Second Car in the Collision?

[Balsam]

Homework Statement

A 1350kg car traveling at 72km/h collides with a slow-moving car of mass 1650kg, also initially traveling south. After the collision, the velocity of the 2 cars together is 24km/h. Determine the initial velocity at which the second car was travelling.

Given: m1=1350kg.
v_i1 = 72km/h=20m/s
v_f1 = 24km/h=6.6666666m/s

m2=1650kg
v_f2=6.6666666m/s

Homework Equations

m1v_i1+m2v_i2=m1v_f1+m2v_f2

The Attempt at a Solution

1350(20)+1650(x)=1350(6.66666666)+1650(6.66666666)
27000+1650x=9000+11000
27000+1650x=20000
1650x=-7000
x=-4.24242424m/s=-15.2727272km/h

My answer was right except for the negative sign. Does the negative sign mean I did something wrong, because I didn't put negative signs infront of the velocity values in my calculations to indicate direction. What did I do wrong?

 

[gneill]

It looks like there's something wrong with the question itself if what you've posted is a true reproduction of it. I notice that the question does not specify the direction of travel for the first car but then says that the second car is "also initially traveling south". Why "also"? It looks like the question has been edited (poorly).

Your calculations look fine for the information given (although you should really do something about presenting so many superfluous digits in results; Round to a suitable number of digits to match the given significant figures).

Perhaps someone updated the problem by changing a value or two (my guess is the mass of the second car) and didn't verify that the resulting velocity for it would turn out to be negative.

 

[Balsam]

It looks like there's something wrong with the question itself if what you've posted is a true reproduction of it. I notice that the question does not specify the direction of travel for the first car but then says that the second car is "also initially traveling south". Why "also"? It looks like the question has been edited (poorly).

Your calculations look fine for the information given (although you should really do something about presenting so many superfluous digits in results; Round to a suitable number of digits to match the given significant figures).

Perhaps someone updated the problem by changing a value or two (my guess is the mass of the second car) and didn't verify that the resulting velocity for it would turn out to be negative.

The answer in the book is the same magnitude but the direction is [North]. And, I copied the question word for word from the textbook

 

[Balsam]

The answer in the book is the same magnitude but the direction is [North]. And, I copied the question word for word from the textbook

How does it make sense that the direction of the answer is [north] when the textbook question explicitly states that the initial velocity of the car is south?

 

[gneill]

The answer in the book is the same magnitude but the direction is [North]. And, I copied the question word for word from the textbook

So, North is the opposite direction of South. It's a 180° direction change. That means your answer is fine, you just have to interpret the sign change as the direction change.

 

[Balsam]

So, North is the opposite direction of South. It's a 180° direction change. That means your answer is fine, you just have to interpret the sign change as the direction change.

Oh, but then why does the textbook say that the initial velocity is in the south direction and the answer is north?

 

[gneill]

How does it make sense that the direction of the answer is [north] when the textbook question explicitly states that the initial velocity of the car is south?

Technically, a velocity value can be positive or negative. In common language we don't use negative velocities when describing motion, we just say something is moving at a certain speed in a certain direction. But mathematically it is fine to say that something is moving with a negative speed in a given direction, which implies that it is actually moving in the opposite direction. It's something to be aware of when dealing with the mathematics.

 

[Balsam]

Technically, a velocity value can be positive or negative. In common language we don't use negative velocities when describing motion, we just say something is moving at a certain speed in a certain direction. But mathematically it is fine to say that something is moving with a negative speed in a given direction, which implies that it is actually moving in the opposite direction. It's something to be aware of when dealing with the mathematics.

Thanks