Question

A person walks due north for 1 km then west for 1.5km then southwest for 2.5km. Draw each displacement then find the total displacement using head to tail method.

An Airplane flys southwest for 100km then east for 75km. What is the total displacement using component method of addition?

Please show all work

Answer 1

Given

A person walks due north for 1 km then west for 1.5km

then southwest for 2.5km

writing the vector in component form

let vectors are A for 1 km, B for 1.5 km , C for

2.5 km , R is final vector  

A = 1 cos 90 i + 1 sin 90 j = 0 i + 1 j

B = 1.5 cos 180 i + 1.5 sin 180 j = -1.5 i + 0 j

adding the vectors A,B ==> D = -1.5 km i + 1 km j

now the vector c = 2.5 cos225 i + 2.5 sin 225 j = -1.768 km i -1.768 km j

there fore the resultant displacement is  

R = C+D

R = (-1.5-1.768)km i + (1 -1.768 )km j = -3.268 km i -0.768 km j

the magnitude is  

R = sqrt((-3.268)^2+(-0.768)^2) km = 3.357 km

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due south west the displacement is 100 km and due east is 75 km

let A = 100 cos 225 i + 100 sin 225 j = -70.710km i -70.710km j

and B = 75 cos 0 i + 75 sin 0 j = 75 km i + 0 km j

A+B = (-70.710+75)km i +(-70.710+0)km j = 4.29 km i -70.710 km j

the magnitude is sqrt(4.29^2+(-70.710)^2)= 70.84 km

the total displacement is 70.84 km