Answer:
The maximum depth of water in the tank shall be 22.784 centimeters.
Explanation:
The maximum height will be reached when the rate at which water enters the tank will be equal to the rate at which water will leave the vessel.
Let us assume that the maximum level of water in the tank is 'h' meters
Since the hole is at bottom
According to Torricelli's Law the speed at which the water shall leave the tank equals
Thus the rate at which water leaves the tank will be equal to
Thus equating the rate of inlet of water and rate of outlet of water we get:
Answer:
Explanation:
For this interesting problem, we use the definition of centripetal acceleration
a = v² / r
angular and linear velocity are related
v = w r
we substitute
a = w² r
the rectangular body rotates at an angular velocity w
We locate the points, unfortunately the diagram is not shown. In this case we have the axis of rotation in a corner, called O, in one of the adjacent corners we call it A and the opposite corner A
the distance OB = L₂
the distance AB = L₁
the sides of the rectangle
It is indicated that the acceleration in in A and B are related
we substitute the value of the acceleration
w² r_A = n r_B
the distance from the each corner is
r_B = L₂
r_A =
we substitute
\sqrt{L_1^2 + L_2^2} = n L₂
L₁² + L₂² = n² L₂²
L₁² = (n²-1) L₂²
Answer:
The average speed of the earth in its orbit is
Explanation:
The average distance between the Earth and the Sun is .
The average speed of the earth in its orbit can be found by the next equation :
(1)
Where r is the radius and T is the period.
In this case, the orbit of the Earth can be considered as a circle
() instead of an ellipse.
It takes 1 year to the Earth to make one revolution around the Sun. Therefore, its period will be 365.25 days.
Notice that to express the period in terms of seconds, the following is needed:
⇒
Then, equation 1 can be used: