Question

what is the horizontal component of a vector that has a magnitude of 6.78 and is at an angle of 71 degrees? 0/1 77.78 1.35 3 64.22 2.2 what is the vertical component of a vector that has a magnitude of 6.78 and is at an angle of 71 degrees? 0/1 6.41 77.78 4 2.2 64.22

Explanation:

Step1: Recall vector - component formula

The horizontal component of a vector $\vec{v}$ with magnitude $|\vec{v}|$ and angle $\theta$ with the positive x - axis is given by $v_x=|\vec{v}|\cos\theta$. The vertical component is given by $v_y = |\vec{v}|\sin\theta$. Here $|\vec{v}| = 6.78$ and $\theta=71^{\circ}$.

Step2: Calculate the horizontal component

$v_x=6.78\times\cos(71^{\circ})$. Since $\cos(71^{\circ})\approx0.326$, then $v_x = 6.78\times0.326\approx2.2$.

Step3: Calculate the vertical component

$v_y=6.78\times\sin(71^{\circ})$. Since $\sin(71^{\circ})\approx0.946$, then $v_y=6.78\times0.946\approx6.41$.

Answer:

What is the horizontal component of a vector that has a magnitude of 6.78 and is at an angle of 71 degrees?
E. 2.2
What is the vertical component of a vector that has a magnitude of 6.78 and is at an angle of 71 degrees?
A. 6.41