# A dog searching for a bone walks 3.5 m southeast, then 8.2 m at an angle 30° north of east. Find the magnitude of the dog's resultant vector.

###### Question:

3.5 m southeast, then 8.2 m at an

angle 30° north of east.

Find the magnitude of the dog's

resultant vector.

## Answers

Answer:Comics636605/20/2020MathematicsMiddle Schoolanswereda dog searching for a bone walks 3.5 m southeast, then 8.2 m at an angle 30 degrees north of east. Find the magnitude of the dog's resultant vector1SEE ANSWERComics6366 is waiting for your help.Add your answer and earn points.OutsideSongAnswer:Step 1: Firstly, we draw both of the axes.Step 2: We then draw a vector of length 3.5 m (theoretical) along the (-x) axis. Step 3: Next, we draw a vector of length 8.2 m from the endpoint towards to top, at an angle of 60° from that point (N.B: 90-30, since it is required to make a 30°∠ with the current vertical; eventually the triangle being formed will be 90° minus the 30°.) Most importantly, the 8.2 m vector should be drawn in such a way so that it is higher than the starting point of the 3.5 m vector. )Step 4: Lastly, we draw a 15 m vector from the endpoint of the 8.2 m vector, running above the original vector, and to the left. This one should be drawn on the left side, and must be situated far enough.∴ Triangle 1 () is of angles 30°, 60° and 90°;On solving for the vertical side (the slope similar to the 3.5 vector), we get(8.2/2) m = 4.1 mNext, we solve for the opposite side via 4.1 × √3= 7.1 mMoving on to Triangle 2 (),top side = (15 - 7.1) m = 7.9 msimilarly, right side = (4.1 - 3.5) m = 0.6 m∴ last side = resultant displacement:⇒ + (0.6)² = 7.9 mand, direction of displacement = arcTan(y/x)= arcTan(0.6/7.9)= 4.3° north of west