# 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?

Tushar Chandra | Certified Educator

calendarEducator since 2010

starTop subjects are Math, Science, and Business

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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## Related Questions

hala718 | Certified Educator

calendarEducator since 2008

starTop subjects are Math, Science, and Social Sciences

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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