# Question FROM Nova Physics

Discussion in 'MCAT Discussions' started by Vanguard23, Apr 12, 2007.

1. ### Vanguard23

Joined:
Sep 5, 2006
Messages:
771
0
Status:
Medical Student
Chapter 8, pg 114(in my copy). The question regarding the collision with the truck and the car. The truck has a mass of 1500kg and is heading east at 20m/s. The car has a mass of 1000kg and is heading north at 10m/s. The book says, using Pythagorean, we obtain a combined momentum of 3.2x10^4 kg*m/s. But how is this? Pythagorean would be (1.0x10^4)^2 + (3.0x10^4)^2, which should come out to be 1.0x10^8 + 9.0x10^8 and end up being 3.0x10^3, if I am correct(which evidentally I'm not).
Could someone give me their insight?

3. ### CptCrunch Senior Member Physician

Joined:
Apr 3, 2005
Messages:
790
17
Status:
Attending Physician
sqrt((1e4)^2+(3e4)^2) = sqrt(1e8+9e8) = sqrt(10e8) = sqrt(10)*10^4 (or just 10^4.5) = 31622.8 ~ 3.2*10^4

4. ### Vanguard23

Joined:
Sep 5, 2006
Messages:
771
0
Status:
Medical Student
Oh,stupid me. I meant to type 3.0x10^4, but still was off by 2.0x10^3.

5. ### scottj72

Joined:
Apr 3, 2007
Messages:
27
1
Status:
Pre-Medical
It is basically a conservation of momentum problem. The total momentum before the collision must be equal to the momentum after the collision.

(1500 kg) (20 m/s) + (1000 kg) (10 m/s) = (1500 kg + 1000 kg)(V)

But all you really need to understand is:

30000 kg.m/s north + 10000 kg.m/s east = final momentum

The reason the Pythagorean Theorum works is because the vector directions are north and east, so 90 degrees. Whew much easier than doing all that sine, cosine and tangent stuff. You can visualize it if you have ever drawn out vector quantitiesin vector addition, and momentum is vector.

(30000)^2 + (10000)^2 = (final momentum)^2

Hope that helps

6. ### scottj72

Joined:
Apr 3, 2007
Messages:
27
1
Status:
Pre-Medical
It is basically a conservation of momentum problem. The total momentum before the collision must be equal to the momentum after the collision.

(1500 kg) (20 m/s) + (1000 kg) (10 m/s) = (1500 kg + 1000 kg)(V)

But all you really need to understand is:

30000 kg.m/s north + 10000 kg.m/s east = final momentum

The reason the Pythagorean Theorum works is because the vector directions are north and east, so 90 degrees. Whew much easier than doing all that sine, cosine and tangent stuff. You can visualize it if you have ever drawn out vector quantitiesin vector addition, and momentum is vector.

(30000)^2 + (10000)^2 = (final momentum)^2

Hope that helps

7. ### scottj72

Joined:
Apr 3, 2007
Messages:
27
1
Status:
Pre-Medical
It is basically a conservation of momentum problem. The total momentum before the collision must be equal to the momentum after the collision.

(1500 kg) (20 m/s) + (1000 kg) (10 m/s) = (1500 kg + 1000 kg)(V)

But all you really need to understand is:

30000 kg.m/s north + 10000 kg.m/s east = final momentum

The reason the Pythagorean Theorum works is because the vector directions are north and east, so 90 degrees. Whew much easier than doing all that sine, cosine and tangent stuff. You can visualize it if you have ever drawn out vector quantitiesin vector addition, and momentum is vector.

(30000)^2 + (10000)^2 = (final momentum)^2

Hope that helps