Question

23 of 30> What are the two possiblities for its z component? Constants Enter your answers using three significant figures separated by a comma You are given a vector in the zy plane that has a magnitude of 85.0 units and a y oomporent of-64.0 units. unts Submit Part B Assuming the z component is known to be posilive, speoity the magnitude of the vector which, if you add it to the original one, would give a resultant wector that is 80.0 units long and points entrely in the -z drection units Reouest Anewer Submit Part C Specily the direction of the vector

Answer 1

A vector lies in x-y plane Therefore Vertical-bar A^sigma Vertical-bar = 85 units A^vector = A_x x^cap + A_y y^cap Vertical-bar A^x Vertical-bar = ? Vertical-bar A^sigma y Vertical-bar = 64 units Ay y^cap = -64 y^cap Therefore A^sigma = a_x x^cap - 64 y^cap Therefore A = squareroot A^2 x + Ay^2 Therefore 85 = squareroot a^2_x + ()64^2 ()85^2 = a^2_x + (64)^2 3129 = A bar_x plusminus 56 x^cap A bar_x = 56 x^cap or A bar_x = -56 x^cap \r\n B (80)^2 = A^2_x + B^2_x A bar = 56 x^cap - 64 y^cap B bar = 64 y^cap + B_x x^cap A bar + B bar = 56 x^cap + B_x x^cap Vertical-bar A bar + B bar Vertical-bar = 80 units Vertical-bar A bar + B bar Vertical-bar = squareroot (56)^2 + B^2_x Therefore (80)^2 = (56)^2 + B_x^2