# Kaplan Physics Question

#### MissMel

##### New Member
10+ Year Member

I am looking over the practice tests for Physics that Kaplan offers.

question:

A billiard ball of mass m and velocity v undergoes an elastic, head-on collision with another billiard ball, also of mass m, which is initially at rest. What is the velocity of the first ball after the collision?

a) 0 b) 1/3v c) 2/3v d) v e) cannot be determined from info given

What do you think the answer is and why? This is a simple problem when numbers are used but there are obviously no numbers and the explanations of their reasons for answers are not always clear to me. I want to see what other ppl get. Thanks!

#### sportsdude00

##### Full Member
10+ Year Member
I am looking over the practice tests for Physics that Kaplan offers.

question:

A billiard ball of mass m and velocity v undergoes an elastic, head-on collision with another billiard ball, also of mass m, which is initially at rest. What is the velocity of the first ball after the collision?

a) 0 b) 1/3v c) 2/3v d) v e) cannot be determined from info given

What do you think the answer is and why? This is a simple problem when numbers are used but there are obviously no numbers and the explanations of their reasons for answers are not always clear to me. I want to see what other ppl get. Thanks!
So, you have an elastic collision, giving the formula:
M1V1i +M2V2i = M1V1f +M2V2f

Given that the second ball is stationary initially, it reduces to:
M1V1i = M1V1f +M2V2f

Also, we know that the masses are equal, so they all cancel.
V1i = V1f+V2f

V1f = V1i - V2f

You do in fact know the initial velocity of the first ball, and you're solving for the final velocity of it. However, the velocity of the second ball is very important in the momentum principle, so without it there is not enough information given. My answer would be (e)

I think that's right, but I'm not sure. Just trying to scrap what I can remember from phys 1. Hope it helped!

#### MissMel

##### New Member
10+ Year Member
That's exactly what I say, but Kaplan says this:
a) 0

explanation:

"An elastic collision means the kinetic energy of the system before the collision equals the kinetic energy after the collision. For all types of collision, both elastic and inelastic, momentum is conserved.

Consider the answer choices. Answer choice A says the velocity of the incoming ball is zero after the collision. The initial momentum is mv, so in order for momentum to be conserved, we require mv2 = mv, where v2 is the velocity of the other ball. This means v2=v.

Notice that this will also guarantee conservation of kinetic energy since the initial kinetic energy is 1/2 mv^2 and the final kinetic energy will now be 1/2mv2^2 = 1/2mv^2. Thus zero final velocity for the incoming ball results in conservation of momentum and conservation of kinetic energy, which means it's the correct value."

-WTF? It looks to me like the person who did the test questions did this problem by starting with the first choice, 0, which does work, but so could other answers. And the explanation is crappy. They set only half of each of the equations - momentum and KE - equal to half of the variables on the other side. Where are the other parts of the eqn???

I'm not trying to be a brat, I'm really annoyed bc I looked over this question a million times trying to see how 0 could be the only answer. I heard the OAT tests a lot on concepts, not using numbers, so if you can't trust Kaplan's test answers that really sucks. Not to mention, I paid for these tests. So, even if their answer is right, their crappy explanation could be much better.

#### sportsdude00

##### Full Member
10+ Year Member
That's exactly what I say, but Kaplan says this:
a) 0

explanation:

"An elastic collision means the kinetic energy of the system before the collision equals the kinetic energy after the collision. For all types of collision, both elastic and inelastic, momentum is conserved.

Consider the answer choices. Answer choice A says the velocity of the incoming ball is zero after the collision. The initial momentum is mv, so in order for momentum to be conserved, we require mv2 = mv, where v2 is the velocity of the other ball. This means v2=v.

Notice that this will also guarantee conservation of kinetic energy since the initial kinetic energy is 1/2 mv^2 and the final kinetic energy will now be 1/2mv2^2 = 1/2mv^2. Thus zero final velocity for the incoming ball results in conservation of momentum and conservation of kinetic energy, which means it's the correct value."

-WTF? It looks to me like the person who did the test questions did this problem by starting with the first choice, 0, which does work, but so could other answers. And the explanation is crappy. They set only half of each of the equations - momentum and KE - equal to half of the variables on the other side. Where are the other parts of the eqn???

I'm not trying to be a brat, I'm really annoyed bc I looked over this question a million times trying to see how 0 could be the only answer. I heard the OAT tests a lot on concepts, not using numbers, so if you can't trust Kaplan's test answers that really sucks. Not to mention, I paid for these tests. So, even if their answer is right, their crappy explanation could be much better.

Yeah, they could be wrong, but I'm not sure if we're missing something. I agree with their explanation, and it does work out to be zero to given that all the momentum is transferred to the second ball. In most cases that I've studied though, one ball doesnt completely stop...
Either way its good that the question makes you think. The real OAT wont have something so controversial, so you'll be alright. Good luck!