Q:

# mrs.beluga is driving on a snow covered road with a drag factor of 0.2. she brakes suddenly for a deer. The tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet. What is the minimum speed she could have been going?

Accepted Solution

A:
First, we are going to find the radius of the yaw mark. To do that we are going to use the formula: $$r= \frac{c^2}{8m} + \frac{m}{2}$$
where
$$c$$ is the length of the chord
$$m$$ is the middle ordinate
We know from our problem that the tires leave a yaw mark with a 52 foot chord and a middle ornate of 6 feet, so $$c=52$$ and $$m=6$$. Lets replace those values in our formula:
$$r= \frac{52^2}{8(6)} + \frac{6}{2}$$
$$r= \frac{2704}{48} +3$$
$$r= \frac{169}{3} +3$$
$$r= \frac{178}{3}$$

Next, to find the minimum speed, we are going to use the formula: $$s= \sqrt{15fr}$$
where
$$f$$ is drag factor
$$r$$ is the radius
We know form our problem that the drag factor is 0.2, so $$f=0.2$$. We also know from our previous calculation that the radius is $$\frac{178}{3}$$, so $$r= \frac{178}{3}$$. Lets replace those values in our formula:
$$s= \sqrt{(15)(0.2)( \frac{178}{3}) }$$
$$s= \sqrt{178}$$
$$s=13.34$$ mph

We can conclude that Mrs. Beluga's minimum speed before she applied the brakes was 13.34 miles per hour.