Question

A grasshopper makes four jumps. The displacement vectors are (1) 38.0 cm, due west; (2) 27.0 cm, 42.0 ° south of west; (3) 20.0 cm, 66.0 ° south of east; and (4) 23.0 cm, 77.0 ° north of east. Find (a) the magnitude and (b) direction of the resultant displacement. Express the direction as a positive angle with respect to due west.

Answer 1

To find:We have to find magnitude and displacement of resultant displacement .

Approach : As displacement is a vector quantity so resultant displacement is vector sum of all displacements and for this we can break individual displacements into rectangular components and then add them .

Solution :

Lets break these displacement vectors into rectangular components ( along East and along north)

First displacement :

Second displacement:

Third displacement :

Fourth displacement :

So net displacement is :

So magnitude of displacepent is

...........Answer part A

Diection can be given in form of

or

.............Answer part b