Question

(problem reference m.1) four displacement vectors are shown in the figure. the magnitudes of the displacements are: ( a = 2.25 , \text{cm} ), ( b = 6.35 , \text{cm} ), ( c = 5.47 , \text{cm} ), and ( d = 4.19 , \text{cm} ).
what is the y - component of vector ( vec{c} )?

• ( -2.48 , \text{cm} )
• ( 2.48 , \text{cm} )
• ( -4.87 , \text{cm} )
• ( -1.39 , \text{cm} )
• ( -5.47 , \text{cm} )

Explanation:

Step1: Determine the formula for the y - component of a vector

The formula for the y - component of a vector \(\vec{C}\) is \(C_y = -C\sin\theta\) (negative because the vector is in the fourth - quadrant where the y - direction is negative). Here, \(C = 5.47\) cm and \(\theta=27.0^{\circ}\).

Step2: Calculate the y - component

Substitute the values into the formula: \(C_y=-5.47\times\sin(27.0^{\circ})\).
We know that \(\sin(27.0^{\circ})\approx0.454\).
So, \(C_y=-5.47\times0.454=-2.48\) cm.

Answer:

-2.48 cm