Question

a velocity of 10m/s has its y - components 5root2 m/s. Calculate its x - component.

Answer 1

the resultant velocity is given by the formula v=$\sqrt{ x^{2} + y^{2} }$
so, 10m/s=$\sqrt{ x^{2} + (5 \sqrt{2} )^{2} }$
squaring on both sides, 100=x²+50
thus, x²=50
         x=5√2
hope it helps....

Answer 2

The answer to the question is $5\sqrt{2}\ m/s$ i.e the x-component of the velocity is $5\sqrt{2}\ m/s$

CALCULATION:

The resultant is given as v= 10 m/s

The y-component is given as $v_{y}\ =\ 5\sqrt{2}\ m/s$

We are asked to calculate the x-component i.e $v_{x}$

$v_{x}\ and\ v_{y}$ are mutually perpendicular to each other.

From parallelogram law of vector addition we know that -

                                        $R^2=A^2+B^2+2ABcos\theta$

Here, $\theta$ is the angle between them.

                                        $R^2=A^2+B^2$    [∵ $\theta=90^0]$

Putting the above values we get-

                                        $v^2=v_{x}^2+v_{y}^2$

                                       ⇒ $v_{x}^2=v^2-v_{y}^2$

                                               $=\ 10^2-(5\sqrt{2})^2$

                                               $=\ 100-50$

                                      ⇒ $v_{x}\ =\sqrt{50}\ m/s$

                                              $=5\sqrt{2}\ m/s$   [ans]