A Pendulum 45cm long swings through a vertical angle of 30degrees. Find the distance of the altitude through which the pendulum bob rises.
(I couldn't find this answer either :\ but can anyone please please help me! And if you can, can you also write the equation on how you found the answer cos' I can learn from it. Thanks)
but in the answer book that has no way on how to find it says its wrong.. the answer of it is 1.533cm
The wording of the question leaves it open to two interpretation.
Is the total swing 30º or is the swing from the vertical 30º ?
bob took the second interpretation, why don't you try
45cos15º and then follow the other steps of bob's answer ?
Cos15=A/45
=43.46666...
45-43.4666=1.533cm
draw the diagram. You know the angle and length, what is the vertical? 45cos30.
Now what is the height of the rise?
45-45cos30
Well, let's see if I can swing into action and help you with this problem!
To find the distance of the altitude through which the pendulum bob rises, we can use a little trigonometry. The vertical angle of 30 degrees forms a right triangle with the length of the pendulum as the hypotenuse.
Using the sine function, we can write the equation:
sin(30°) = opposite / hypotenuse
We know the hypotenuse, which is 45 cm, and we want to find the opposite side (the altitude through which the pendulum bob rises). Rearranging the equation, we have:
opposite = sin(30°) * 45 cm
Plugging in the values, we get:
opposite = 0.5 * 45 cm
= 22.5 cm
So, the distance of the altitude through which the pendulum bob rises is 22.5 cm.
I hope that helps, and if my explanation didn't swing with you, feel free to let me know and I'll try to come up with something better!
To find the distance of the altitude through which the pendulum bob rises, we can use trigonometry.
The pendulum forms a right triangle when it swings through its maximum angle. The length of the pendulum (L) is the hypotenuse of this right triangle, the vertical distance (d) is the opposite side, and the horizontal distance (h) is the adjacent side.
We can use the sine function to relate the angle and the opposite side:
sin(angle) = opposite / hypotenuse
In this case, the angle is 30 degrees and the hypotenuse is the length of the pendulum, which is 45 cm:
sin(30) = d / 45
Next, we rearrange the equation to solve for d:
d = sin(30) * 45
Now we can calculate the value of sin(30) using a scientific calculator or an online calculator.
sin(30) is approximately 0.5, so the equation becomes:
d = 0.5 * 45
Simplifying the equation:
d = 22.5 cm
Therefore, the distance of the altitude through which the pendulum bob rises is 22.5 cm.