(8%) Problem 3: Suppose you first walk 10.S m in a direction 20 Degree west of n

Question

(8%) Problem 3: Suppose you first walk 10.S m in a direction 20 Degree west of north and then 225 m in a direction 400 south of west as shown in the figure. Part (a) What is the component of your displacement in the x-direction, in meters? Part (b) What is the component of your displacement in the y-direction, in meters? Part (c) How far are you from your starting point in meters? Part (d) What is the angle of a line connecting your starting position to your final position, measured South of West, in degrees?

Explanation / Answer

given,

first walk = 10.5 m toward 20 degree west of north

then 22.5 m toward 40 degree south of west

sum of x components = -10.5 * sin(20) + (-22.5 * cos(40))

sum of x components = -20.8272 m

displacement in x direction = -20.8272 m

sum of y components = 10.5 * cos(20) - 22.5 * sin(40)

sum of y components = -4.5959 m

displacement in y direction = -4.5959 m

resultant = sqrt(20.8272^2 + 4.5959^2)

distance from starting point = 21.328 m

angle = tan^-1(4.5959 / 20.8272)

angle = 12.44 degree south of west

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