Answer:
4.80 seconds
Explanation:
The velocity of sound is obtained from;
V= 2d/t
Where;
V= velocity of sound = 329.2 ms-1
d= distance from the wall = 790.5 m
t= time = the unknown
t= 2d/V
t= 2 × 790.5/ 329.2
t= 4.80 seconds
To solve this problem we will use the kinematic formula for the final velocity.
![V_f_x = V_0_x + a_xt](https://tex.z-dn.net/?f=V_f_x%20%3D%20V_0_x%20%2B%20a_xt)
The final speed is 0 at the moment the player stops.
The time until it stops is 1.3 s
The initial speed is 200 feet / s Note (check the speed units in the problem statement, 200ft / s is very much and 200ft / h is very small)
Then, we clear the formula.
![a_x = \frac{(Vfx-V0x)}{t}\\ a_x = \frac{(0-200)}{1.3}\\ a_x = -153.5 ft / s ^ 2](https://tex.z-dn.net/?f=a_x%20%3D%20%5Cfrac%7B%28Vfx-V0x%29%7D%7Bt%7D%5C%5C%20a_x%20%3D%20%5Cfrac%7B%280-200%29%7D%7B1.3%7D%5C%5C%20a_x%20%3D%20-153.5%20ft%20%2F%20s%20%5E%202)
Because the player is slowing down, the acceleration goes in the opposite direction to the player's movement, and that is why it is negative.
To answer part b) we use the following formula.
![Vf ^ 2 = Vo ^ 2 + 2a * (x_2 - x_1)\\\\ (x_2 - x_1)= \frac{(V_f ^ 2-V_0 ^ 2)}{2a}\\\\ (x_2 - x_1)= \frac{(0-200 ^ 2)}{- 2 * 153.5}\\\\ (x_2 - x_1)= 130.29 feet](https://tex.z-dn.net/?f=Vf%20%5E%202%20%3D%20Vo%20%5E%202%20%2B%202a%20%2A%20%28x_2%20-%20x_1%29%5C%5C%5C%5C%20%28x_2%20-%20x_1%29%3D%20%5Cfrac%7B%28V_f%20%5E%202-V_0%20%5E%202%29%7D%7B2a%7D%5C%5C%5C%5C%20%28x_2%20-%20x_1%29%3D%20%5Cfrac%7B%280-200%20%5E%202%29%7D%7B-%202%20%2A%20153.5%7D%5C%5C%5C%5C%20%28x_2%20-%20x_1%29%3D%20130.29%20feet)
Answer:
The intensity of the electric field is
![|E|=10654.37 \:N/C](https://tex.z-dn.net/?f=%7CE%7C%3D10654.37%20%5C%3AN%2FC)
Explanation:
The electric field equation is given by:
![|E|=k\frac{q}{d^{2}}](https://tex.z-dn.net/?f=%7CE%7C%3Dk%5Cfrac%7Bq%7D%7Bd%5E%7B2%7D%7D)
Where:
- k is the Coulomb constant
- q is the charge at 0.4100 m from the balloon
- d is the distance from the charge to the balloon
As we need to find the electric field at the location of the balloon, we just need the charge equal to 1.99*10⁻⁷ C.
Then, let's use the equation written above.
![|E|=(9*10^{9})\frac{1.99*10^{-7}}{0.41^{2}}](https://tex.z-dn.net/?f=%7CE%7C%3D%289%2A10%5E%7B9%7D%29%5Cfrac%7B1.99%2A10%5E%7B-7%7D%7D%7B0.41%5E%7B2%7D%7D)
![|E|=10654.37 \:N/C](https://tex.z-dn.net/?f=%7CE%7C%3D10654.37%20%5C%3AN%2FC)
I hope it helps you!
Answer:
Stephen hawking if his family were scientists
1.
Answer:
Part a)
![\rho = 1.35 \times 10^{-5}](https://tex.z-dn.net/?f=%5Crho%20%3D%201.35%20%5Ctimes%2010%5E%7B-5%7D%20)
Part b)
![\alpha = 1.12 \times 10^{-3}](https://tex.z-dn.net/?f=%5Calpha%20%3D%201.12%20%5Ctimes%2010%5E%7B-3%7D)
Explanation:
Part a)
Length of the rod is 1.60 m
diameter = 0.550 cm
now if the current in the ammeter is given as
![i = 18.7 A](https://tex.z-dn.net/?f=i%20%3D%2018.7%20A)
V = 17.0 volts
now we will have
![V = I R](https://tex.z-dn.net/?f=V%20%3D%20I%20R)
![17.0 = 18.7 R](https://tex.z-dn.net/?f=17.0%20%3D%2018.7%20R)
R = 0.91 ohm
now we know that
![R = \rho \frac{L}{A}](https://tex.z-dn.net/?f=R%20%3D%20%5Crho%20%5Cfrac%7BL%7D%7BA%7D)
![0.91 = \rho \frac{1.60}{\pi(0.275\times 10^{-2})^2}](https://tex.z-dn.net/?f=0.91%20%3D%20%5Crho%20%5Cfrac%7B1.60%7D%7B%5Cpi%280.275%5Ctimes%2010%5E%7B-2%7D%29%5E2%7D)
![\rho = 1.35 \times 10^{-5}](https://tex.z-dn.net/?f=%5Crho%20%3D%201.35%20%5Ctimes%2010%5E%7B-5%7D%20)
Part b)
Now at higher temperature we have
![V = I R](https://tex.z-dn.net/?f=V%20%3D%20I%20R)
![17.0 = 17.3 R](https://tex.z-dn.net/?f=17.0%20%3D%2017.3%20R)
R = 0.98 ohm
now we know that
![R = \rho \frac{L}{A}](https://tex.z-dn.net/?f=R%20%3D%20%5Crho%20%5Cfrac%7BL%7D%7BA%7D)
![0.98 = \rho' \frac{1.60}{\pi(0.275\times 10^{-2})^2}](https://tex.z-dn.net/?f=0.98%20%3D%20%5Crho%27%20%5Cfrac%7B1.60%7D%7B%5Cpi%280.275%5Ctimes%2010%5E%7B-2%7D%29%5E2%7D)
![\rho' = 1.46 \times 10^{-5}](https://tex.z-dn.net/?f=%5Crho%27%20%3D%201.46%20%5Ctimes%2010%5E%7B-5%7D%20)
so we will have
![\rho' = \rho(1 + \alpha \Delta T)](https://tex.z-dn.net/?f=%5Crho%27%20%3D%20%5Crho%281%20%2B%20%5Calpha%20%5CDelta%20T%29)
![1.46 \times 10^{-5} = 1.35 \times 10^{-5}(1 + \alpha (92 - 20))](https://tex.z-dn.net/?f=1.46%20%5Ctimes%2010%5E%7B-5%7D%20%3D%201.35%20%5Ctimes%2010%5E%7B-5%7D%281%20%2B%20%5Calpha%20%2892%20-%2020%29%29)
![\alpha = 1.12 \times 10^{-3}](https://tex.z-dn.net/?f=%5Calpha%20%3D%201.12%20%5Ctimes%2010%5E%7B-3%7D)
2.
Answer:
Part a)
![i = 1.55 A](https://tex.z-dn.net/?f=i%20%3D%201.55%20A)
Part b)
![v_d = 1.4 \times 10^{-4} m/s](https://tex.z-dn.net/?f=v_d%20%3D%201.4%20%5Ctimes%2010%5E%7B-4%7D%20m%2Fs)
Explanation:
Part a)
As we know that current density is defined as
![j = \frac{i}{A}](https://tex.z-dn.net/?f=j%20%3D%20%5Cfrac%7Bi%7D%7BA%7D)
now we have
![i = jA](https://tex.z-dn.net/?f=i%20%3D%20jA)
Now we have
![j = 1.90 \times 10^6 A/m^2](https://tex.z-dn.net/?f=j%20%3D%201.90%20%5Ctimes%2010%5E6%20A%2Fm%5E2)
![A = \pi(\frac{1.02 \times 10^{-3}}{2})^2](https://tex.z-dn.net/?f=A%20%3D%20%5Cpi%28%5Cfrac%7B1.02%20%5Ctimes%2010%5E%7B-3%7D%7D%7B2%7D%29%5E2)
so we will have
![i = 1.55 A](https://tex.z-dn.net/?f=i%20%3D%201.55%20A)
Part b)
now we have
![j = nev_d](https://tex.z-dn.net/?f=j%20%3D%20nev_d)
so we have
![n = 8.5 \times 10^{28}](https://tex.z-dn.net/?f=n%20%3D%208.5%20%5Ctimes%2010%5E%7B28%7D)
![e = 1.6 \times 10^{-19} C](https://tex.z-dn.net/?f=e%20%3D%201.6%20%5Ctimes%2010%5E%7B-19%7D%20C)
so we have
![1.90 \times 10^6 = (8.5 \times 10^{28})(1.6 \times 10^{-19})v_d](https://tex.z-dn.net/?f=1.90%20%5Ctimes%2010%5E6%20%3D%20%288.5%20%5Ctimes%2010%5E%7B28%7D%29%281.6%20%5Ctimes%2010%5E%7B-19%7D%29v_d)
![v_d = 1.4 \times 10^{-4} m/s](https://tex.z-dn.net/?f=v_d%20%3D%201.4%20%5Ctimes%2010%5E%7B-4%7D%20m%2Fs)