Vector problem with traveling car

[ThomasMagnus]

A car is driven 215 km west then 85km south west. Find the resultant displacement (magnitude and direction) from the Point of origin.

My solution would be to resolve the two vectors into components. How can I do this if there is no angle given?

In the solution to the problem, they are using 45 degrees as the angle. Where does the 45 come from? If you are not given an angle are you to assume the angle is 45 degrees?

Thanks!

 

[chris_0101]

The angle is given, its just not in numerical form. The question states 85km south west, that south west indicates 45 degrees.

hope this helps

-Chris

 

[WolfeSieben]

For vectors, the total displacement is from the origin to the final location.

Try drawing this problem out.

For example, you drive 5km east, and 5 km south. Our human logic states that we drove 10 km. however, this isn't the displacement. We've only displaced ourselves by the hypotenuse of the 2 directions. In this case our 10 km 'drive' displaced us: the root of 5^2 + 5^2 (Pythagoras theory: A^2 + B^2 = C^2) = 7.07km.

To summarize, we drove for 10km, but were only displaced by 7.07km.

Hope this helps.

 

[ThomasMagnus]

Great thanks!

 

[rwisz]

I would approach this problem by first determining the angle of the second vector using the given information. Since the car is traveling southwest, we know that it is moving in a direction that is between west and south, making the angle between the two vectors approximately 45 degrees. This angle can also be confirmed using trigonometric functions such as tangent or cosine.

Once the angle is determined, we can then use basic vector addition to find the resultant displacement. We can resolve the two vectors into their x and y components, and then add them together to find the total displacement. The magnitude of the resultant displacement can be found using the Pythagorean theorem, and the direction can be determined using trigonometric functions.

In cases where an angle is not explicitly given, we can use logical reasoning and knowledge of basic trigonometry to estimate the angle and solve the problem. It is important to note that this estimation may not always be accurate, and it is best to confirm the angle with additional information if possible. In cases where no additional information is available, we can use the estimated angle as a reasonable approximation.