MATH SOLVE

2 months ago

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: [tex]r= \frac{c^2}{8m} + \frac{m}{2} [/tex]

where

[tex]c[/tex] is the length of the chord

[tex]m[/tex] 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 [tex]c=52[/tex] and [tex]m=6[/tex]. Lets replace those values in our formula:

[tex]r= \frac{52^2}{8(6)} + \frac{6}{2} [/tex]

[tex]r= \frac{2704}{48} +3[/tex]

[tex]r= \frac{169}{3} +3[/tex]

[tex]r= \frac{178}{3} [/tex]

Next, to find the minimum speed, we are going to use the formula: [tex]s= \sqrt{15fr} [/tex]

where

[tex]f[/tex] is drag factor

[tex]r[/tex] is the radius

We know form our problem that the drag factor is 0.2, so [tex]f=0.2[/tex]. We also know from our previous calculation that the radius is [tex] \frac{178}{3} [/tex], so [tex]r= \frac{178}{3}[/tex]. Lets replace those values in our formula:

[tex]s= \sqrt{(15)(0.2)( \frac{178}{3}) } [/tex]

[tex]s= \sqrt{178} [/tex]

[tex]s=13.34[/tex] mph

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

where

[tex]c[/tex] is the length of the chord

[tex]m[/tex] 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 [tex]c=52[/tex] and [tex]m=6[/tex]. Lets replace those values in our formula:

[tex]r= \frac{52^2}{8(6)} + \frac{6}{2} [/tex]

[tex]r= \frac{2704}{48} +3[/tex]

[tex]r= \frac{169}{3} +3[/tex]

[tex]r= \frac{178}{3} [/tex]

Next, to find the minimum speed, we are going to use the formula: [tex]s= \sqrt{15fr} [/tex]

where

[tex]f[/tex] is drag factor

[tex]r[/tex] is the radius

We know form our problem that the drag factor is 0.2, so [tex]f=0.2[/tex]. We also know from our previous calculation that the radius is [tex] \frac{178}{3} [/tex], so [tex]r= \frac{178}{3}[/tex]. Lets replace those values in our formula:

[tex]s= \sqrt{(15)(0.2)( \frac{178}{3}) } [/tex]

[tex]s= \sqrt{178} [/tex]

[tex]s=13.34[/tex] mph

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