an ant crawls on a tabletop, moves 2cm east, turns 3cm 40 degrees north of east and finally.....?

Question

help me solve this:

an ant crawls on a tabletop, moves 2cm east, turns 3cm 40 degrees north of east and finally moves 2.5cm north. what is the ants total displacement??

Answer 1

Use a scale drawing. Using 1 cm = 2 cm,

1. Draw a horizontal line AB, 4 cm, from left to right (A represents the beginning, right represents East). Use broken lines to extend AB by about 5 cm.
2. Using a protractor, measure 40 degrees at B, from the broken line,(going obliquely upward), so that the angle formed with AB is 140 degrees.
Let the end of this be C. Draw BC = 6 cm.
3. From C, draw a vertical line upwards (i.e. North) 5 cm long, to end at D.
4. The displacement is represented by AD. Measure AD and divide by 2 (the scale) to get the distance. Measure angle DAB to get the direction. You should get approximately 6.2 cm NE (i.e. 6.2 cm 45 degrees North of East)

It is assumed that by "turns 3 cm 40 degrees", the turn was abrupt resulting in a straight line and not an arc between B and C.