In phase would mean both waves are at a positive peak, out of phase would mean one is at a positive whilst the other is at a negative. Out of phase would mean the waves cancel each other out
Answer:
![\theta = 106.3 degree](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20106.3%20degree)
Explanation:
As we know that
![\vec w = -\hat i + 7\hat j](https://tex.z-dn.net/?f=%5Cvec%20w%20%3D%20-%5Chat%20i%20%2B%207%5Chat%20j)
![\vec v = 7\hat i - \hat j](https://tex.z-dn.net/?f=%5Cvec%20v%20%3D%207%5Chat%20i%20-%20%5Chat%20j)
also we know that
![\vec v. \vec w = -14](https://tex.z-dn.net/?f=%5Cvec%20v.%20%5Cvec%20w%20%3D%20-14)
it is given as
![\vec v. \vec w = (-\hat i + 7\hat j).(7\hat i - \hat j)](https://tex.z-dn.net/?f=%5Cvec%20v.%20%5Cvec%20w%20%3D%20%28-%5Chat%20i%20%2B%207%5Chat%20j%29.%287%5Chat%20i%20-%20%5Chat%20j%29)
![\vec v. \vec w = - 7 - 7 = -14](https://tex.z-dn.net/?f=%5Cvec%20v.%20%5Cvec%20w%20%3D%20-%207%20-%207%20%3D%20-14)
also we can find the magnitude of two vectors as
![|v| = \sqrt{(-1)^2 + (7)^2}](https://tex.z-dn.net/?f=%7Cv%7C%20%3D%20%5Csqrt%7B%28-1%29%5E2%20%2B%20%287%29%5E2%7D)
![|v| = \sqrt{50}](https://tex.z-dn.net/?f=%7Cv%7C%20%3D%20%5Csqrt%7B50%7D)
similarly we have
![|w| = \sqrt{(7^2) + (-1)^2}](https://tex.z-dn.net/?f=%7Cw%7C%20%3D%20%5Csqrt%7B%287%5E2%29%20%2B%20%28-1%29%5E2%7D)
![|w| = \sqrt{50}](https://tex.z-dn.net/?f=%7Cw%7C%20%3D%20%5Csqrt%7B50%7D)
now we know the formula of dot product as
![\vec v. \vec w = |v||w| cos\theta](https://tex.z-dn.net/?f=%5Cvec%20v.%20%5Cvec%20w%20%3D%20%7Cv%7C%7Cw%7C%20cos%5Ctheta)
![-14 = (\sqrt{50})^2cos\theta](https://tex.z-dn.net/?f=-14%20%3D%20%28%5Csqrt%7B50%7D%29%5E2cos%5Ctheta)
![\theta = cos^{-1}(\frac{-14}{50})](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20cos%5E%7B-1%7D%28%5Cfrac%7B-14%7D%7B50%7D%29)
![\theta = 106.3 degree](https://tex.z-dn.net/?f=%5Ctheta%20%3D%20106.3%20degree)
Newtons 1st law of motion states that the object will continue to move at its present speed and direction until an outside force acts upon it.
So unless the objects inside the car are restrained, they will continue moving at whatever speed the car is traveling at, even if the car is stopped by a crash.
Answer: q2 = -0.05286
Explanation:
Given that
Charge q1 = - 0.00325C
Electric force F = 48900N
The electric field strength experienced by the charge will be force per unit charge. That is
E = F/q
Substitute F and q into the formula
E = 48900/0.00325
E = 15046153.85 N/C
The value of the repelled second charge will be achieved by using the formula
E = kq/d^2
Where the value of constant
k = 8.99×10^9Nm^2/C^2
d = 5.62m
Substitutes E, d and k into the formula
15046153.85 = 8.99×10^9q/5.62^2
15046153.85 = 284634186.5q
Make q the subject of formula
q2 = 15046153.85/ 28463416.5
q2 = 0.05286
Since they repelled each other, q2 will be negative. Therefore,
q2 = -0.05286
Let's call
![m=565~g=0.565~kg](https://tex.z-dn.net/?f=m%3D565~g%3D0.565~kg)
the mass of the glider and
![m_w=7\cdot12~g =84~g=0.084~kg](https://tex.z-dn.net/?f=m_w%3D7%5Ccdot12~g%20%3D84~g%3D0.084~kg)
the total mass of the seven washers hanging from the string.
The net force on the system is given by the weight of the hanging washers:
![F_{net} = m_w g](https://tex.z-dn.net/?f=F_%7Bnet%7D%20%3D%20m_w%20g)
For Newton's second law, this net force is equal to the product between the total mass of the system (which is
![m+m_w](https://tex.z-dn.net/?f=m%2Bm_w)
) and the acceleration a:
![F_{net}=(m+m_w)a](https://tex.z-dn.net/?f=F_%7Bnet%7D%3D%28m%2Bm_w%29a)
So, if we equalize the two equations, we get
![m_w g = (m+m_w)a](https://tex.z-dn.net/?f=m_w%20g%20%3D%20%28m%2Bm_w%29a)
and from this we can find the acceleration: