Answer:
608.4m/s
Explanation:
We are given that
Mass of Sleigh,M=1200 kg
Speed of Sleigh,u=322 m/s
Speed of jet,u'=680 m/s
Mass of jet,m=4800 kg
Total mass=M+m=1200+4800=6000 kg
We have to find the final velocity of the two objects after the collision.
The collision is inelastic .
By using law of conservation of momentum
![Mu+mu'=(m+M)v](https://tex.z-dn.net/?f=Mu%2Bmu%27%3D%28m%2BM%29v)
Using the formula
![1200\times 322+4800\times 680=6000v](https://tex.z-dn.net/?f=1200%5Ctimes%20322%2B4800%5Ctimes%20680%3D6000v)
![6000v=3650400](https://tex.z-dn.net/?f=6000v%3D3650400)
![v=\frac{3650400}{6000}](https://tex.z-dn.net/?f=v%3D%5Cfrac%7B3650400%7D%7B6000%7D)
![v=608.4m/s](https://tex.z-dn.net/?f=v%3D608.4m%2Fs)
Hence, the final velocity of two objects after the collision=608.4m/s
<span>
Elecromagnetic waves can travel through a vacuum, but a mechanical wave cannot.
Mechanical waves can only exist in a medium, such as air or water. Electromagnetic
waves behave like waves and particles, but mechanical waves only behave
like waves. </span>
If we connect Gabe's current position to the top of the building, to the bottom of the building and back to Gabe, we form a right triangle with the height of 250 m and the angle opposite to the height being equal to 19°. If we let x be his distance from the building, we use the trigonometric formula,
tan 19° = x/250 m
The value of x from the equation is 86.08 m. Thus, the answer is 86.08 m.
Answer:
(a) The equivalent resistance is 18.06 Ω
(b) The current in each resistor is 0.665 A
Explanation:
Given;
first resistor, R₁ = 2.25 Ω
second resistor, R₂ = 5.90 Ω
third resistor, R₃ = 9.91 Ω
Equivalent resistance;
![R_T = R_1 + R_2+ R_3\\\\](https://tex.z-dn.net/?f=R_T%20%3D%20R_1%20%2B%20R_2%2B%20R_3%5C%5C%5C%5C)
2.25 Ω + 5.90 Ω + 9.91 Ω
18.06 Ω
The current in each resistor;
For series connection, current is the same in every resistor.
V = I(R₁ + R₂ + R₃)
![V = IR_T\\\\I = \frac{V}{R_T} \\\\I = \frac{12}{18.06} \\\\I = 0.665 \ A](https://tex.z-dn.net/?f=V%20%3D%20IR_T%5C%5C%5C%5CI%20%3D%20%5Cfrac%7BV%7D%7BR_T%7D%20%5C%5C%5C%5CI%20%3D%20%5Cfrac%7B12%7D%7B18.06%7D%20%5C%5C%5C%5CI%20%3D%200.665%20%5C%20A)
The variation of entropy of a substance is given by
![\delta S = \frac{\delta Q}{T}](https://tex.z-dn.net/?f=%5Cdelta%20S%20%3D%20%20%5Cfrac%7B%5Cdelta%20Q%7D%7BT%7D%20)
(1)
where
![\delta Q](https://tex.z-dn.net/?f=%5Cdelta%20Q)
is the heat exchanged in the process
T is the absolute temperature at which the transformation occurs.
The process in the problem is the solidification of the liquid Gallium, which releases an amount of heat equal to:
![\delta Q = m L_f](https://tex.z-dn.net/?f=%5Cdelta%20Q%20%3D%20m%20L_f)
where m is the mass of the substance and
![L_f = 80.1 J/g](https://tex.z-dn.net/?f=L_f%20%3D%2080.1%20J%2Fg)
is the latent heat of fusion of Gallium. Using m=64.0 g, we find
![\delta Q= m L_f = (64.0 g)(80.1 J/g)=-5126.4 J](https://tex.z-dn.net/?f=%5Cdelta%20Q%3D%20m%20L_f%20%3D%20%2864.0%20g%29%2880.1%20J%2Fg%29%3D-5126.4%20J)
where the negative sign means the Gallium is releasing heat to the environment.
Now we can use equation (1) to find the variation of entropy, but first we need to convert the temperature into Kelvin:
![T=29.8^{\circ} + 273.15 = 302.95 K](https://tex.z-dn.net/?f=T%3D29.8%5E%7B%5Ccirc%7D%20%2B%20273.15%20%3D%20302.95%20K)
And so the variation of entropy is
![\delta S = \frac{\delta Q}{T}= \frac{-5126.4 J}{302.95 K}=-16.92 J](https://tex.z-dn.net/?f=%5Cdelta%20S%20%3D%20%20%5Cfrac%7B%5Cdelta%20Q%7D%7BT%7D%3D%20%5Cfrac%7B-5126.4%20J%7D%7B302.95%20K%7D%3D-16.92%20J%20%20)
and the negative sign means the entropy in the process is decreasing.