Question

Define an xy coordinate system on the face of an analog clock with the origin at the center. What is the horizontal component of a 3 cm long hour hand at 10:00 am?

Answer 1

Calculation of the angle between each hour.

$\theta_{div}=\frac{360^{0}}{12div}=30^{0}/div$

From the direction of the positive x-axis until 10am there are 5 divisions, therefore the degrees are

$\theta=5div*30^{0}/div=150^{0}$

Now, the horizontal component is given by

$cos\theta=\frac{r_{x}}{r}\\ r_{x}=r*cos\theta\\$

Numerically evaluating

$r_{x}=3.00cm*cos(150^{0})\\ r_{x}=-2.60cm$

The horizontal component of the long hand at 10:00am is

$\boxed{r_{x}=-2.60cm}$