Answer:
<em>The density of a substance is the relationship between the mass of the substance and how much space it takes up</em>
Explanation:
thats it take my word hope thats what u meant
Answer:
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Answer:
(a) 83475 MW
(b) 85.8 %
Explanation:
Output power = 716 MW = 716 x 10^6 W
Amount of water flows, V = 1.35 x 10^8 L = 1.35 x 10^8 x 10^-3 m^3
mass of water, m = Volume x density = 1.35 x 10^8 x 10^-3 x 1000
= 1.35 x 10^8 kg
Time, t = 1 hr = 3600 second
T1 = 25.4° C, T2 = 30.7° C
Specific heat of water, c = 4200 J/kg°C
(a) Total energy, Q = m x c x ΔT
Q = 1.35 x 10^8 x 4200 x (30.7 - 25.4) = 3 x 10^12 J
Power = Energy / time
Power input =
Power input = 83475 MW
(b) The efficiency of the plant is defined as the ratio of output power to the input power.
![\eta =\frac{Power output}{Power input}](https://tex.z-dn.net/?f=%5Ceta%20%3D%5Cfrac%7BPower%20output%7D%7BPower%20input%7D)
![\eta =\frac{716}{83475}=0.858](https://tex.z-dn.net/?f=%5Ceta%20%3D%5Cfrac%7B716%7D%7B83475%7D%3D0.858)
Thus, the efficiency is 85.8 %.
The time it takes for a ball to complete the trip is given to be 4.10 s. This implies that the trip going up of the ball is equal to 2.05 s. Using this time to determine the initial speed, we have,
Vf = Vo - gt
Vf is the final speed which is equal to 0 on the topmost location of the ball.
0 = Vo - (9.8 m/s²)(2.05 s)
Vo = 20.09 m/s
At 0.5 s,
Vf = 20.09 m/s - (9.8 m/s²)(0.5 s)
Vf = 15.19 m/s
Thus, the speed of the ball when the height is in level with the top of the flagpole is 15.19 m/s.
It is possible to demonstrate that the maximum distance occurs when the angle at which the projectile is fired is
![\theta = 45^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%20%3D%2045%5E%7B%5Ccirc%7D)
.
In fact, the laws of motions on both x- and y- directions are
![S_x(t)= v_0 cos \theta t](https://tex.z-dn.net/?f=S_x%28t%29%3D%20v_0%20cos%20%5Ctheta%20t)
![S_y(t)= v_0 \sin \theta t - \frac{1}{2} gt^2](https://tex.z-dn.net/?f=S_y%28t%29%3D%20v_0%20%5Csin%20%5Ctheta%20t%20-%20%20%5Cfrac%7B1%7D%7B2%7D%20gt%5E2)
From the second equation, we get the time t at which the projectile hits the ground, by requiring
![S_y(t)=0](https://tex.z-dn.net/?f=S_y%28t%29%3D0%20)
, and we get:
![t= \frac{2 v_0 \sin \theta}{g}](https://tex.z-dn.net/?f=t%3D%20%5Cfrac%7B2%20v_0%20%5Csin%20%5Ctheta%7D%7Bg%7D%20)
And inserting this value into Sx(t), we find
![S_x(t) = 2 \frac{v_0^2}{g} \sin \theta \cos \theta= \frac{v_0^2}{g} \sin (2\theta)](https://tex.z-dn.net/?f=S_x%28t%29%20%3D%202%20%20%5Cfrac%7Bv_0%5E2%7D%7Bg%7D%20%20%5Csin%20%5Ctheta%20%5Ccos%20%5Ctheta%3D%20%5Cfrac%7Bv_0%5E2%7D%7Bg%7D%20%5Csin%20%282%5Ctheta%29)
And this value is maximum when
![\theta=45^{\circ}](https://tex.z-dn.net/?f=%5Ctheta%3D45%5E%7B%5Ccirc%7D)
, so this is the angle at which the projectile reaches its maximum distance.
So now we can take again the law of motion on the x-axis
![S_x(t)= \frac{v_0^2}{g} \sin (2\theta)](https://tex.z-dn.net/?f=S_x%28t%29%3D%20%20%5Cfrac%7Bv_0%5E2%7D%7Bg%7D%20%5Csin%20%282%5Ctheta%29)
And by using
![S_x = 26 km=26000 m](https://tex.z-dn.net/?f=S_x%20%3D%2026%20km%3D26000%20m)
, we find the value of the initial velocity v0: