two cars A and B are 600 meters apart car A travels due east at some speed per on a collision course with car b which travels due west at half speed as car A if the two cars fatally collide with each other in 5 seconds how fast was car A going?

Car A was going at 80 m/s

Explanation:

Let's call "x" the unknown speed of car A. In such case, the speed of car B would be x/2.

We proceed to describe the distance covered by car A (dA) in the 5 seconds it took to collide:  dA = speed * time = x * 5 = 5 x

Now the distance covered by car B (dB) in the same time would be:

dB = speed * time = (x/2) * 5 = 5 x / 2

Now, we know that the distance that separated both cars was 600 meters, so the addition of what car A covered plus what car B covered must equal 600 m, and in equation form:

dA + dB = 600

5 x + 5 x / 2 = 600

combining like terms:

15 x / 2 = 600

multiplying both sides by 2:

15 x = 1200

divide both sides by 15:

x = 80 m/s

This is the speed of car A.

come closer and become far apart and become steam/gas

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west