Kinetic energy as a vector?

[Tokspor]

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I came across a momentum and kinetic energy question today involving two objects heading towards each other from opposite directions. The object coming from the right, m1, is 250 kg and traveling at 5 m/s. The object from the left, m2, is also 250 kg but traveling at 2 m/s. The text then says the collision is completely inelastic.

I used 0.5(m1v1)^2 + 0.5(m2v2)^2 to find the total kinetic energy before the collision. However, the text I used said this was wrong. It said I should have used -0.5(m2v2)^2 for the kinetic energy of m2 since its velocity, v2, is in the opposite direction of v1.

I thought kinetic energy was scalar and so direction doesn't need to be considered to find the total kinetic energy of the system. Is the text mistaken or am I?

 

[G1SG2]

I came across a momentum and kinetic energy question today involving two objects heading towards each other from opposite directions. The object coming from the right, m1, is 250 kg and traveling at 5 m/s. The object from the left, m2, is also 250 kg but traveling at 2 m/s. The text then says the collision is completely inelastic.

I used 0.5(m1v1)^2 + 0.5(m2v2)^2 to find the total kinetic energy before the collision. However, the text I used said this was wrong. It said I should have used -0.5(m2v2)^2 for the kinetic energy of m2 since its velocity, v2, is in the opposite direction of v1.

I thought kinetic energy was scalar and so direction doesn't need to be considered to find the total kinetic energy of the system. Is the text mistaken or am I?

I think the book is wrong. I did a similar problem in TPR's In-Class Compendium. A truck and a car were driving toward each other from opposite directions. The car's KE was "KE", and I was asked to find the total KE of the cars before the collision. The truck was twice the mass of the car, so if the car's KE was "KE", then the truck's KE would be 2KE (since KE=1/2mv^2, and if you double the mass you double the KE), giving a total KE of 3KE, which is the right answer for that problem. You're right-energy is a scalar. Now, if you were asked to find the MOMENTUM before the collision, then you would've used -m1v1 for the vehicle travelig in the - x direction.

lol, is this an EK problem?

 

[odellus]

The book is wrong. You are right, rest assured.

This kind of thing happens so much it is scary.