What is the distance between the cars? The distance between 2 cars when they start is 10 km. The first car moves at a speed of 40 km/h towards the right perpendicular to the initial line joining the...

What is the distance between the cars?

The distance between 2 cars when they start is 10 km. The first car moves at a speed of 40 km/h towards the right perpendicular to the initial line joining the two cars. The other car is stationary. What is the distance between the two cars after 2 hours?

 

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hala718 eNotes educator | Certified Educator

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We will calculate the distance between the first car and the starting point.

Let the car begins at A and move perpendicularly to B.

The speed if 40 km/h

Then the distance after 2 hours is : D = Speed * Time = 40*2 = 80 km

Then the distance between A and B is 80.

Now we will assume that the other car is at C.

We know that the length of AC is the initial distance between the cars which is 10 km

==> Then AC = 10.

Now we have a right angle triangle ABC such that:

AB = 80

AC = 10

We nee to find the distance between both cars after 2 hours which is the length of the line BC.

==> BC^2 = AB^2 + AC^2 = 10^2 + 80^2 = 6500

==> BC = sqrt6500 = 80.62 km ( approx.)

Then the distance between the cars after 2 hours is 80.62 km.

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justaguide eNotes educator | Certified Educator

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The cars are initially at a distance of 10 km from each other. One of them starts to move towards the right in a direction perpendicular to the line joining the cars initially. As the speed of the car is 40 km/h after 2 hours it has moved a distance of 80 km.

Now the distance between the two cars can be calculated using the Pythagorean Theorem. The two perpendicular sides are of a length 10 km and 80 km. The distance separating the cars is given by sqrt(10^2 + 80^2)

=> sqrt (100 + 6400)

=> sqrt (6500)

=> 10* sqrt 65

The distance between the cars after 2 hours is 10*sqrt 65 km.

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