Question

find the components of v_tot along the x and y axes in the figure below, where θ = 25.0° and v_tot = 7.76 m/s. v_tot = v_a + v_b v_tot,x = v_tot,y =

Explanation:

Step1: Find x - component formula

The x - component of a vector $\vec{v}_{tot}$ with magnitude $v_{tot}$ and angle $\theta$ with the x - axis is given by $v_{tot,x}=v_{tot}\cos\theta$.

Step2: Substitute values

We are given that $v_{tot} = 7.76$ m/s and $\theta = 25.0^{\circ}$. So, $v_{tot,x}=7.76\cos(25.0^{\circ})$.
Using a calculator, $\cos(25.0^{\circ})\approx0.9063$, then $v_{tot,x}=7.76\times0.9063\approx7.03$ m/s.

Step3: Find y - component formula

The y - component of a vector $\vec{v}_{tot}$ with magnitude $v_{tot}$ and angle $\theta$ with the x - axis is given by $v_{tot,y}=v_{tot}\sin\theta$.

Step4: Substitute values

We know $v_{tot} = 7.76$ m/s and $\theta = 25.0^{\circ}$. So, $v_{tot,y}=7.76\sin(25.0^{\circ})$.
Using a calculator, $\sin(25.0^{\circ})\approx0.4226$, then $v_{tot,y}=7.76\times0.4226\approx3.28$ m/s.

Answer:

$v_{tot,x}\approx7.03$ m/s, $v_{tot,y}\approx3.28$ m/s