Question

A velocity vector 40°below the positive x-axis has a y-component of -10 m/s. What is the value of its x-component?

Short answer

The value of its x-component is 11.92 m/s

Step-by-step solution

Step 1. Given information

The given values are,

The angle is $\theta ={40}^0$

y- component of the velocity is $v_y=-10m/s$

Step 2. Calculate the value of velocity v

Let velocity vector is $\overrightarrow{v}$.

y- component of the velocity is

$v_y=-v\sin \theta$

Put the value of y- component of the velocity

$-10=-v\sin {40}^0$

$v=\frac{10}{\sin {40}^0}$

Step 3. Calculate the value of x- component 

We know that,

x- component of the velocity is

$v_x=v\cos \theta$

Put the value of v and $\theta$

$v_x=\frac{10}{\sin {40}^o}\times \cos {40}^o$

$v_x=11.92m/s$