How to find total displacement

[nevik]

A motorist drives south at 24.0 m/s for 3.00 min, then turns west and travels at 25.0 m/s for 3.00 min, and finally travels northwest at 30.0 m/s for 1.00 min. For this 7.00 min trip, find the following values.

a) total vector displacement and degrees south of west.

For the displacement I try to find the total displacement southwest of the first two vectors which should be sqrt(72^2+75^2) and get 103.966. From there I draw a line 30m northwest of it and at the endpoint of that line I draw another line to the origin. This 3rd line should be the hypotenuse of the triangle so I try adding 103.96^2 + 30^2 and taking the square root of it to get 107.28m but when I enter it on webassign it says I'm ORDERS OF MAGNITUDE WRONG? No idea what I'm doing wrong here and I don't think I can solve the second part without the first part.

 

[LowlyPion]

Welcome to PF.

Careful with your units.

Minutes are a little different than seconds.

 

[nlightner]

I would approach this problem by first breaking down the motion into individual vectors and then using vector addition to find the total displacement.

For the first vector, the motorist is traveling south at 24.0 m/s for 3.00 min. This gives us a displacement of 72.0 m south.

For the second vector, the motorist turns west and travels at 25.0 m/s for 3.00 min. This gives us a displacement of 75.0 m west.

For the third vector, the motorist travels northwest at 30.0 m/s for 1.00 min. Since this is a diagonal direction, we can use the Pythagorean theorem to find the displacement. The diagonal distance is given by the hypotenuse of the triangle formed by the two previous displacements. So we can use the equation c^2 = a^2 + b^2, where c is the diagonal distance, a is the displacement south, and b is the displacement west. Plugging in the values, we get c^2 = (72.0 m)^2 + (75.0 m)^2 = 10368 m^2. Taking the square root, we get a diagonal distance of 103.966 m northwest.

Now, to find the total displacement, we can use vector addition. This involves adding the individual vectors together to get the resultant vector. In this case, we have three vectors, so we can add them in any order. Let's add the first two vectors first: (72.0 m south) + (75.0 m west) = 99.0 m southwest. Now, we can add this resultant vector to the third vector: (99.0 m southwest) + (103.966 m northwest) = 4.966 m south, 4.966 m west.

Therefore, the total displacement is 4.966 m south and 4.966 m west. To find the angle south of west, we can use trigonometry. The tangent of the angle is given by the opposite side (4.966 m south) divided by the adjacent side (4.966 m west). So tanθ = 4.966 m south/4.966 m west = 1. Therefore, the angle is tan^-1(1) = 45 degrees south of west.

I hope this explanation helps you understand the process of finding