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Novay_Z [31]
3 years ago
8

Two towns are 1300 miles apart. A group of hikers starts from each town and walks down the trail toward each other. They meet af

ter a total hiking time of 240 hours. If one group travels 2 1/2 miles per hour slower than the other group, find the rate of each group.

Mathematics
1 answer:
Leto [7]3 years ago
5 0
240(v+2.5)=1300-240v

240v+600=1300-240v

480v=1900

v=95/24

v-2.5=v-5/2

95/24-60/24=35/24

So the faster group travels at 95/24 mph (≈3.96 mph) and the slower group travels at 35/24 mph (≈1.46mph)

check...

240(95/24)=950 miles from the origin...

1300-240(35/24)=950 miles from the origin...

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A 4-lb. force acting in the direction of (vector) 4,-2 moves an object just over 7ft from point (0,4) to (5,-1). Find the work d
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To solve this problem, we have to find the net displacement and the net force and the multiply the dot product together and get the work done.

The work done on moving the object is 27ft*lbs

<h3>Work done in moving the object from point A to point B</h3>

To find the work done on this object, let's find the net force on the object.

Data;

  • force = 4lb
  • direction = 4, -2
  • displacement = 7ft
  • direction = (0, 4) to (5,1)

The unit vector of the force is

\sqrt{4^2 +(-2)^2} =\sqrt{16 + 4} = \sqrt{20}

\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} }

The net force acting on the object is

F = 4(\frac{4}{\sqrt{20} }, \frac{-2}{\sqrt{20} })\\F= (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } )

The displacement on the object is 7ft through (0,4) to (5, -1)

The unit vector on displacement is

\sqrt{5^2 + (-1-4)^2} = \sqrt{25+25} = \sqrt{50}

\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }

The net displacement will be

7(\frac{5}{\sqrt{50} }, \frac{-5}{\sqrt{50} }) = \frac{35}{\sqrt{50} }, \frac{-35}{50}

The work done will be F.d

w = f. d \\

w = (\frac{16}{\sqrt{20} }, \frac{-8}{\sqrt{20} } ) * \frac{35}{\sqrt{50} }, \frac{-35}{50}\\w = 17.71+ 8.854\\w = 26.567 = 27ft*lbs

The work done on moving the object is 27ft*lbs

Learn more on work done on an object here;

brainly.com/question/26152883

#SPJ1

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