Using the conservation of momentumwhere momentum = mass x velocity
so the let x be the initial velocity of the ball B
(30 kg) (-10 m/s) + (10 kg) (x) = (30 kg) (30 m/s) + ( 10 kg) (-10 m/s)
-300 + 10 x = 900 - 10010x = 900 - 100 + 30010x = 1100x = 1100 / 10x = 110 m/s
Answers:
a) ![\hat F=(0.83,-0.55) N](https://tex.z-dn.net/?f=%5Chat%20F%3D%280.83%2C-0.55%29%20N)
b) ![\hat D=(-0.44,-0.89) m](https://tex.z-dn.net/?f=%5Chat%20D%3D%28-0.44%2C-0.89%29%20m)
c) ![\hat V=(-0.47,0.88) m/s](https://tex.z-dn.net/?f=%5Chat%20V%3D%28-0.47%2C0.88%29%20m%2Fs)
Explanation:
A unit vector is a vector whose magnitude (length) is equal to 1. This kind of vector is identified as
and the way to calculate is as follows:
![\hat v=\frac{\vec v}{|v|}](https://tex.z-dn.net/?f=%5Chat%20v%3D%5Cfrac%7B%5Cvec%20v%7D%7B%7Cv%7C%7D)
Where:
is the vector
is the magnitude of the vector
Having this information clarified, let's begin with the answers:
a) Force Vector
![\vec F=(9.0 \hat i - 6.0 \hat j) N](https://tex.z-dn.net/?f=%5Cvec%20F%3D%289.0%20%5Chat%20i%20-%206.0%20%5Chat%20j%29%20N)
Magnitude of
:
![|F|=\sqrt{(9.0 \hat i)^{2}+(-6.0 \hat j)^{2 }}N=10.81 N](https://tex.z-dn.net/?f=%7CF%7C%3D%5Csqrt%7B%289.0%20%5Chat%20i%29%5E%7B2%7D%2B%28-6.0%20%5Chat%20j%29%5E%7B2%20%7D%7DN%3D10.81%20N)
<u />
<u>Unit vector:</u>
![\hat F=\frac{\vec F}{|F|}](https://tex.z-dn.net/?f=%5Chat%20F%3D%5Cfrac%7B%5Cvec%20F%7D%7B%7CF%7C%7D)
![\hat F=\frac{9.0}{10.81} N-\frac{6.0}{10.81}N](https://tex.z-dn.net/?f=%5Chat%20F%3D%5Cfrac%7B9.0%7D%7B10.81%7D%20N-%5Cfrac%7B6.0%7D%7B10.81%7DN)
![\hat F=(0.83,-0.55) N](https://tex.z-dn.net/?f=%5Chat%20F%3D%280.83%2C-0.55%29%20N)
b) Displacement Vector
![\vec D=(-4.0 \hat i - 8.0 \hat j) m](https://tex.z-dn.net/?f=%5Cvec%20D%3D%28-4.0%20%5Chat%20i%20-%208.0%20%5Chat%20j%29%20m)
Magnitude of
:
![|D|=\sqrt{(-4.0 \hat i)^{2}+(-8.0 \hat j)^{2 }}m=8.94 m](https://tex.z-dn.net/?f=%7CD%7C%3D%5Csqrt%7B%28-4.0%20%5Chat%20i%29%5E%7B2%7D%2B%28-8.0%20%5Chat%20j%29%5E%7B2%20%7D%7Dm%3D8.94%20m)
<u />
<u>Unit vector:</u>
![\hat D=\frac{\vec D}{|D|}](https://tex.z-dn.net/?f=%5Chat%20D%3D%5Cfrac%7B%5Cvec%20D%7D%7B%7CD%7C%7D)
![\hat D=\frac{-4.0}{8.94} Nm+\frac{-8.0}{8.94}m](https://tex.z-dn.net/?f=%5Chat%20D%3D%5Cfrac%7B-4.0%7D%7B8.94%7D%20Nm%2B%5Cfrac%7B-8.0%7D%7B8.94%7Dm)
![\hat D=(-0.44,-0.89) m](https://tex.z-dn.net/?f=%5Chat%20D%3D%28-0.44%2C-0.89%29%20m)
c) Velocity Vector
![\vec V=(-3.50 \hat i + 6.50 \hat j) m/s](https://tex.z-dn.net/?f=%5Cvec%20V%3D%28-3.50%20%5Chat%20i%20%2B%206.50%20%5Chat%20j%29%20m%2Fs)
Magnitude of
:
![|V|=\sqrt{(-3.50 \hat i)^{2}+(6.50 \hat j)^{2}}m/s=7.38 m/s](https://tex.z-dn.net/?f=%7CV%7C%3D%5Csqrt%7B%28-3.50%20%5Chat%20i%29%5E%7B2%7D%2B%286.50%20%5Chat%20j%29%5E%7B2%7D%7Dm%2Fs%3D7.38%20m%2Fs)
<u />
<u>Unit vector:</u>
![\hat V=\frac{\vec V}{|V|}](https://tex.z-dn.net/?f=%5Chat%20V%3D%5Cfrac%7B%5Cvec%20V%7D%7B%7CV%7C%7D)
![\hat V=\frac{-3.50}{7.38} m/s+\frac{6.50}{7.38}m/s](https://tex.z-dn.net/?f=%5Chat%20V%3D%5Cfrac%7B-3.50%7D%7B7.38%7D%20m%2Fs%2B%5Cfrac%7B6.50%7D%7B7.38%7Dm%2Fs)
![\hat V=(-0.47,0.88) m/s](https://tex.z-dn.net/?f=%5Chat%20V%3D%28-0.47%2C0.88%29%20m%2Fs)
The answer is "the earths rotation"
When two or more waves combine to produce a new wave, that's 'interference'.
-- If the new wave has larger displacements (amplitude), then it's <em>CON</em>structive interference.
-- If the new wave has smaller displacements (amplitude), then it's DEstructive interference.