A) what is the x component net displacement? B) what is the y component net disp

Question

A) what is the x component net displacement? B) what is the y component net displacement? C) what is the z component net displacement?
D) What is the magnitude of the net displacement? E) What angle does the net displacement (vector) make with the horizontal plane? F) By how much does the Aggie's gravitational potential energy increase from O to C?
Take g = 10 m/s^2 Suppose that an 50-kg Aggie walks from origin O: 10 *first, straight to point A displaced 50 m due East & 10 m vertically down * second, from A to B displaced a further 71 m NW & 20 m vertically up, and * third, from B to C displaced another 40 m due North & 10 m vertically down hoose +x-,y-, & z-axes along the East, North, and vertically up directions, respectively

Explanation / Answer

The displacement vectors as mentioned in the question:

d1 = 50 (i^) + 10 (k^)

d2 = - 71 cos45° (i^) + 71 sin45° (j^) + 20 (k^)

d3 = 40 (j^) + 10 (k^)

(A) The x component net displacement,

  dx  = 50 - 71 cos45° = 0 m ............Option (a)

(B) The y component net displacement,

  dy  = 40 + 71 sin45° = 90 m ............Option (h)

(C) The z component net displacement,

  dz  = 10 + 20 + 10 = 40 m ............Option (c)

(D) The magnitude of the net displace ]ment,

d  = sqrt [ (dx)^2 + (dy)^2 + (dz)^2 ]

     = sqrt [ (0)^2 + (90)^2 + (40)^2 ] =   99 m  ............Option (i)

(E)   The angle which the net displacement (vector) makes with the horizontal plane,

    = tan^-1 [ dz / d ] = tan^-1 [ 40 / 99 ] = tan^-1 [0.404] = 22° ............Option (c)

(F) The amount by which the Aggie's gravitational potential energy increases from O to C,

  U  = m*g*dz = 50*(9.8)*40 = 20,000 J = 20 kJ ............Option (c)

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