Explanation:
Given that,
Displacement in ice block, ![d=14i-11j](https://tex.z-dn.net/?f=d%3D14i-11j)
Force exerted by water, ![F=158i-179j](https://tex.z-dn.net/?f=F%3D158i-179j)
To find,
Work done by the force during the displacement.
Solve,
We know that the product of force and displacement is called work done. It is also equal to the dot product of force and displacement as :
![W=F.d](https://tex.z-dn.net/?f=W%3DF.d)
![W=(158i-179j).(14i-11j)](https://tex.z-dn.net/?f=W%3D%28158i-179j%29.%2814i-11j%29)
We know that, i.i = j.j = k.k = 1
![W=2212+1969=4181\ J](https://tex.z-dn.net/?f=W%3D2212%2B1969%3D4181%5C%20J)
So, the work done by the force on the block during the displacement is 4181 Joules.
The correct answer you should be looking for is complementary. :)
Answer:
changing the direction in which a force is exerted
when a hole is made at the bottom of the container then water will flow out of it
The speed of ejected water can be calculated by help of Bernuolli's equation and Equation of continuity.
By Bernoulli's equation we can write
![Po + \frac{1}{2}\rho v_1^2 + \rho g h = Po + \frac{1}{2}\rho v_2^2 + \rho g *0](https://tex.z-dn.net/?f=Po%20%2B%20%5Cfrac%7B1%7D%7B2%7D%5Crho%20v_1%5E2%20%2B%20%5Crho%20g%20h%20%3D%20Po%20%2B%20%5Cfrac%7B1%7D%7B2%7D%5Crho%20v_2%5E2%20%2B%20%5Crho%20g%20%2A0)
Now by equation of continuity
![A_1v_1 = A_2v_2](https://tex.z-dn.net/?f=A_1v_1%20%3D%20A_2v_2)
![\pi (0.2)^2 v_1 = \pi (0.01)^2 v_2](https://tex.z-dn.net/?f=%5Cpi%20%280.2%29%5E2%20v_1%20%3D%20%5Cpi%20%280.01%29%5E2%20v_2)
from above equation we can say that speed at the top layer is almost negligible.
![v_1 = 0](https://tex.z-dn.net/?f=v_1%20%3D%200)
now again by equation of continuity
![\rho g h = \frac{1}{2} \rho v^2](https://tex.z-dn.net/?f=%5Crho%20g%20h%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%5Crho%20v%5E2)
![v = \sqrt{2 g h}](https://tex.z-dn.net/?f=%20v%20%3D%20%5Csqrt%7B2%20g%20h%7D)
here we have
![h = h_1 - h_2](https://tex.z-dn.net/?f=%20h%20%3D%20h_1%20-%20h_2)
![h = 0.50 - 0.03 = 0.47m](https://tex.z-dn.net/?f=h%20%3D%200.50%20-%200.03%20%3D%200.47m)
now speed is given by
![v = \sqrt{2* 9.8 * 0.47}](https://tex.z-dn.net/?f=%20v%20%3D%20%5Csqrt%7B2%2A%209.8%20%2A%200.47%7D)
![v = 3.03 m/s](https://tex.z-dn.net/?f=v%20%3D%203.03%20m%2Fs)