Question

As you stop your car at a traffic light, a pebble becomes wedged between the tire treatds. When you start off, the distance of the pebble from the pav

Solid Geometry
ANSWERED
asked 2020-12-28
As you stop your car at a traffic light, a pebble becomes wedged between the tire treatds. When you start off, the distance of the pebble from the pavement varies sinusoidally with the distance you have traveled. Assume the diameter of the wheel is 24 inches. Find the first two distances you have traveled when the pebble in the tire tread is 11 inches above the pavement.

Answers (1)

2020-12-29

image
This answer may be more complicated than needed but here itis. First we need to set up a right triangle. The hypot. is 12in because that is the radius. second we know that one leg is 1 in use pyth. theor. to solve for third leg
\(\displaystyle{b}=\sqrt{{{12}^{{2}}-{1}^{{2}}}}=\sqrt{{{143}}}\)
now we can use tha law of sines to figure out theta
\(\displaystyle{\frac{{{\sin{{\left(\theta\right)}}}}}{{\sqrt{{{143}}}}}}={\frac{{{\sin{{\left({90}\right)}}}}}{{{12}}}}\)
So \(\displaystyle\theta={{\sin}^{{-{1}}}{\left({\sin{{\left({90}\right)}}}\cdot{\frac{{\sqrt{{{143}}}}}{{{12}}}}\right)}}\)
\(\displaystyle\theta\) is approximately \(\displaystyle{85.2}^{\circ}\)
Now we know theta is the central angle so we canb plug itinto the formula
\(\displaystyle\text{Arc Length}={\left({\frac{{\text{central angle}}}{{{360}^{\circ}}}}\right)}\cdot{2}\pi{r}\)
\(\displaystyle={\left({\frac{{{85.2}}}{{{360}^{\circ}}}}\right)}\cdot{2}\pi{12}\)
\(\displaystyle={17.844}\)
Second distance
\(\displaystyle{360}-{85.2}={274.8}\)
\(\displaystyle{\left({\frac{{{274.8}}}{{{360}}}}\right)}\cdot{2}\pi{12}={57.55}\)
This is the actual arc length.

0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2021-04-18
A tire 2.00ft in diameter is placed on a balancing machine,where it is spun so that its tread is moving at a constant speed of 60.0 mi/h. A small stone is stuck in the tread of the tire. What isthe acceleration of the stone as the tire is being balanced?
asked 2021-06-18
A bicycle tire has a diameter of 27 inches. How far does the bike travel along the ground when the wheel rotates once?
asked 2021-05-09
The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus
\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)
where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.
Part A:
Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.
Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.
Part B:
A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).
Assume the following:
The top speed is limited by air drag.
The magnitude of the force of air drag at these speeds is proportional to the square of the speed.
By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?
Express the percent increase in top speed numerically to two significant figures.
asked 2021-04-13
As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.
a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.
...