Final answer:
The height an object is pulled back on a pendulum can be calculated using the length of the pendulum and the cosine of the angle of displacement: h = L - Lcos(θ), applying basic trigonometry.
Step-by-step explanation:
To find the formula for the height an object is pulled back on a pendulum, you must use basic trigonometry and the known values: the length of the pendulum (L) and the angle (θ) at which the pendulum bob is lifted from the vertical.
You can visualize the pendulum in its lifted position as forming a right-angled triangle with the length of the pendulum as the hypotenuse. The vertical height (h) can be calculated using the cosine of the angle θ:
h = L - Lcos(θ)
This happens because the adjacent side of the right-angled triangle, which lies along the pendulum string, has a length of Lcos(θ). Hence, the difference between the pendulum length and this adjacent side gives us the vertical height to which the pendulum bob is lifted.
Also noteworthy is the conservation of energy principle, where gravitational potential energy is converted into kinetic energy. As the pendulum swings down, its potential energy decreases while its kinetic energy increases.