# Pendulum

Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.

Result

l =  25 cm

#### Solution:

$x=2 \ \text{cm} \ \\ o=20 \ \text{cm} \ \\ o_{2}=o/2=20/2=10 \ \text{cm} \ \\ t^2=o_{2}^2 - x^2 \ \\ t=\sqrt{ o_{2}^2 - x^2 }=\sqrt{ 10^2 - 2^2 } \doteq 4 \ \sqrt{ 6 } \ \text{cm} \doteq 9.798 \ \text{cm} \ \\ l^2=(l-x)^2 + t^2 \ \\ l^2=l^2 -2lx + x^2 +t^2 \ \\ 2lx=x^2 +t^2 \ \\ l=(x^2 +t^2)/(2 \cdot \ x)=(2^2 +9.798^2)/(2 \cdot \ 2)=25 \ \text{cm}$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 1 comment:
Tiny
this helps me so much

Tips to related online calculators
Do you want to convert length units?
Pythagorean theorem is the base for the right triangle calculator.

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

1. Cableway
Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
2. Chord 4
I need to calculate the circumference of a circle, I know the chord length c=22 cm and the distance from the center d=29 cm chord to the circle.
3. Two chords
In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords.
4. Stairway
Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm.
5. RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
6. Chord
It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
7. Chord circle
The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
8. Spruce height
How tall was spruce that was cut at an altitude of 8m above the ground and the top landed at a distance of 15m from the heel of the tree?
9. Ethernet cable
Charles and George are passionate gamers and live in houses that are exactly opposite each other across the street, so they can see each other through the windows. They decided that their computers will connect the telephone cable in order to play games t
10. Satin
Sanusha buys a piece of satin 2.4 m wide. The diagonal length of the fabric is 4m. What is the length of the piece of satin?