Find an angle formed by 2 moving vehicles

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brandonbigbook

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Two cars approach a right angled intersection, one traveling south at 40km/h and the other west at 70 km/h. When the faster car is 4 km from the intersection and the other car is 3 km from the intersection what is the angle formed between the two cars?
 
That's a strangely posed question! Since you ask only for the angle at a specific time, the speeds of the cars are completely irrelevant. You have a right triangle with legs of length 3 and 4 km (and so hypotenuse, the straight line distance between the cars, of 5 km). The acute angles of that triangle are arctan(3/4) and arctan(4/3). But I'm not sure which angle you are referring to as "the angle formed between the cars".
 
clarification

The problem shows an intersection with 2 vehicles moving toward the intersection. It says the first vehicle is moving at 40 km/h and is 4 km from the intersection. 2nd vehicle is moving at 3 km/hr and is 3 km from the intersection. The triangle is 90 Degrees and it ask for the angle up by the first car.
 
brandonbigbook said:
The problem shows an intersection with 2 vehicles moving toward the intersection. It says the first vehicle is moving at 40 km/h and is 4 km from the intersection. 2nd vehicle is moving at 3 km/hr and is 3 km from the intersection. The triangle is 90 Degrees and it ask for the angle up by the first car.
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The question is more fun if you consider the angle as a function of time. If you call the position of the first car "x" and the position of the 2nd car "y", then you can use the given speeds to find x(t) and y(t). The tangent of the angle is y/x. How does that ratio change with time??

BTW, I think you have a typo, and the speed of the 2nd is 30 km/hr instead of 3 km/hr. And this is quite fifferent from what you entered the first time.
 
Last edited:
brandonbigbook said:
Two cars approach a right angled intersection, one traveling south at 40km/h and the other west at 70 km/h. When the faster car is 4 km from the intersection and the other car is 3 km from the intersection what is the angle formed between the two cars?
Click to expand...

Angle can ONLY be formed between two LINES.

Two cars make one line - what info do you have about the other line?
 
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