An amateur astronomer grinds a double convex lens whose surfaces have radii of curvature of 40 cm and 60 cm. The glass has an in
1 answer:
Answer:
44.4cm
Explanation:
glass has an index of refraction .n = 1.54
radii of curvature of 40 cm R1 = 40 by
radii of curvature of 600 cm R2 = 60
Now, by lens maker formula
1/f = (n - 1) (1/R1 - 1/R2)
Putting in the given values for n = 1.54 , we get f = 22.2
f = 1 / 0.0225
f = 44.4cm
so, focal length in air will be = 44.4 cm
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a. 0.5 T
- The amplitude A of a simple harmonic motion is the maximum displacement of the system with respect to the equilibrium position
- The period T is the time the system takes to complete one oscillation
During a full time period T, the mass on the spring oscillates back and forth, returning to its original position. This means that the total distance covered by the mass during a period T is 4 times the amplitude (4A), because the amplitude is just half the distance between the maximum and the minimum position, and during a time period the mass goes from the maximum to the minimum, and then back to the maximum.
So, the time t that the mass takes to move through a distance of 2 A can be found by using the proportion
and solving for t we find
b. 1.25T
Now we want to know the time t that the mass takes to move through a total distance of 5 A. SInce we know that
- the mass takes a time of 1 T to cover a distance of 4A
we can set the following proportion:
And by solving for t, we find
The speed of air at the intake area is (m/s).
The continuity equation is used to determine the flow rate at different sections of a pipe or fluid conduit.
The continuity equation is given as;
- Let the intake area = A₁
- Let the velocity of air in intake area = v₁
- Let the area of the test section = A₂
- Velocity of air in test section, v₂ = 10 m/s
The speed of air at the intake area is calculated as follows;
Learn more about continuity equation here: brainly.com/question/14619396
Answer:
<u>6.87 ft/s</u> is the rate at which the top of ladder slides down.
Explanation:
Given:
Length of the ladder is,
Let the top of ladder be at height of 'h' and the bottom of the ladder be at a distance of 'b' from the wall.
Now, from triangle ABC,
AB² + BC² = AC²
Differentiating the above equation with respect to time, 't'. This gives,
In the above equation the term is the rate at which top of ladder slides down and
is the rate at which bottom of ladder slides away.
Now, as per question,
Plug in in equation (1) and solve for
. This gives,
Now, plug in all the given values in equation (2) and solve for
Therefore, the rate at which the top of ladder slide down is 6.87 ft/s. The negative sign implies that the height is reducing with time which is true because it is sliding down.
