Question

A dog in an open field runs 10.0 m east and then 27.0 m in a direction 52.0 degree west of north. In what direction must the dog then run to end up 12.0 m south of her original starting point? How far must the dog then run to end up 12.0 m south of her original starting point? Express your answer with the appropriate units.

Answer 1

here,

the displacement of dog , d1 = 10 i + 27 * (- sin(52) i + cos(52) j) m

d1 = - 11.28 i + 16.6 j m

for final displacemnt to be 12.0 m south of her original starting point , d = - 12 m j - d1

d = 11.28 m - 28.6 j m

A)

direction , theta = arctan(28.6/11.28)

theta = 68.5 degree south of east or 21.5 degree east of south

B)

magnitude , |d| = sqrt(11.28^2 + 28.6^2)

|d| = 26.3 m