Questions on Algebra: Introduction to vectors, addition and scaling answered by real tutors!

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Question 155178This question is from textbook The Physical Universe
: Greetings, I am currently in Physical Science and right off the bat we started on vectors, motion, and Newtons Law. Anyway, I haven't been in a College atmosphere in quite a while. So I need some serious help!!! This will sound silly yet I for some reason can not get it. Here it is: Two cars leave a cross roads at the same time. One heads north at 50Km/h and the other heads east at 70Km/h. How far apart are the cars after 2 hours?This question is from textbook The Physical Universe
: Greetings, I am currently in Physical Science and right off the bat we started on vectors, motion, and Newtons Law. Anyway, I haven't been in a College atmosphere in quite a while. So I need some serious help!!! This will sound silly yet I for some reason can not get it. Here it is: Two cars leave a cross roads at the same time. One heads north at 50Km/h and the other heads east at 70Km/h. How far apart are the cars after 2 hours?
Answer by Earlsdon(3748) About Me  (Show Source):
You can put this solution on YOUR website!
The car headed north at 50 km/hr will have traveled a distance of 100km after 2 hours, right? ((2hrs)*(50km/hr) = 100km.
The car headed east at 70 km/hr will have traveled 140km after 2 hours, ok? (2hrs)*(70km/hr) = 140km.
So you now have two legs of a right triangle in which the base is a vector of magnitude 140km and the height is a vector of magnitude 100km.
The distance between the two cars, after 2 hours of travel, is represented by the hypotenuse of this right triangle.
So you can call upon Pythagoras c^2 = a^2+b^2 to help find the length (distance vector) of the hypotenuse (d).
d^2 = (140)^2+(100)^2
d^2 = 19600+10000
d^2 = 29600
d = sqrt(29600)
d = 172km. Approximately.
This would be a vector whose magnitude is 172.