Question

A man in search of his dog drives first 12.5 mi northeast, then 16.5 mi straight south, and finally 6.31 mi in a direction 32.1

Answer 1

Answer 2

1st disp = 12.5cos(45) i + 12.5sin(45)j = 8.84i+8.84j

2nd disp = -16.5j

3rd disp = 6.31cos(180-32.1)i + 6.31sin(180-32.1) = -5.34i+3.35j

so net disp = (8.84-5.34)i + (8.84-16.5+3.35)j= 3.5i - 4.31j

a)magnitude = sqrt(3.5*3.5+4.31*4.31) = 5.55

b) direction = tan^-1(-4.31/3.5) = 309 degrees counter clockwise with x axis

explained in details

Answer 3

1st disp = 12.5cos(45) i + 12.5sin(45)j = 8.84i+8.84j

2nd disp = -16.5j

3rd disp = 6.31cos(180-32.1)i + 6.31sin(180-32.1) = -5.34i+3.35j

so net disp = (8.84-5.34)i + (8.84-16.5+3.35)j= 3.5i - 4.31j

a)magnitude = sqrt(3.5*3.5+4.31*4.31) = 5.55

b) direction = tan^-1(-4.31/3.5) = 309 degrees counter clockwise with x axis

explained in details