Question

Vector A with arrow has a negative x component 2.70 units in length and a positive y component 1.82 units in length.
(a) Determine an expression for A with arrow in unit-vector notation.
( î + ĵ) units

(b) Determine the magnitude and direction of A with arrow.
magnitude unit(s)
direction ° counterclockwise from the positive x axis

(c) What vector B with arrow when added to vector A with arrow, gives a resultant vector with no x component and a negative y component 3.88 units in length?
( î + ĵ) units

Answer 1

Answer on Question #81101 Physics / Classical Mechanics

Vector A with arrow has a negative $x$ component 2.70 units in length and a positive $y$ component 1.82 units in length.

(a) Determine an expression for A with arrow in unit-vector notation.

(b) Determine the magnitude and direction of A with arrow.

(c) What vector B with arrow when added to vector A with arrow, gives a resultant vector with no $x$ component and a negative $y$ component 3.88 units in length?

Solution:

(a) $\mathbf{A} = (-2.70, 1.82) = -2.70\mathbf{i} + 1.82\mathbf{j}$

(b) $|\mathbf{A}| = \sqrt{A_x^2 + A_y^2} = \sqrt{(-2.70)^2 + 1.82^2} = 3.26, \tan \theta = \frac{A_y}{A_x} = \frac{1.82}{-2.70} = -0.674, \theta = 146{}^\circ$

(c) $\mathbf{A} + \mathbf{B} = (0, -3.88) = -3.88\mathbf{j}, \quad \mathbf{B} = -3.88\mathbf{j} - (-2.70\mathbf{i} + 1.82\mathbf{j}) = 2.70\mathbf{i} - 5.70\mathbf{j}$

Answer:

(a) $-2.70\mathbf{i} + 1.82\mathbf{j}$

(b) $3.26, 146{}^\circ$

(c) $2.70\mathbf{i} - 5.70\mathbf{j}$

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