Question

vector components
given vectors: f = 100 n and v = 100 m/sec, answer questions on
right.
3 multiple answer 2 points
the x - component of v (vx) is equal to:
-50 m/sec
-70 m/sec
70 m/sec
50 m/sec

Explanation:

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

The formula for the x - component of a vector \( V \) is \( V_x=V\cos\theta \), where \( V \) is the magnitude of the vector and \( \theta \) is the angle between the vector and the positive x - axis.

Step2: Identify the values of \( V \) and \( \theta \)

Given \( V = 100\space m/sec \) and \( \theta=120^{\circ}\). We know that \( \cos(120^{\circ})=\cos(180 - 60)^{\circ}=-\cos(60^{\circ})\) and \( \cos(60^{\circ}) = 0.5\).

Step3: Calculate \( V_x \)

Substitute \( V = 100\) and \( \cos(120^{\circ})=- 0.5\) into the formula \( V_x=V\cos\theta \). So \( V_x=100\times(-0.5)=- 50\space m/sec\)

Answer:

-50 m/sec