- #1

Istiak

- 158

- 10

- Homework Statement:
- Find value of ##\theta## when ##V_x=V_y##

- Relevant Equations:
- Vector

The picture may be blurry. I couldn't take more less blurry picture hence, giving it.

The question is : Find value of ##\theta## when ##V_x## component and ##V_y## component same.

I was using a simple equation of vector.

$$C=\sqrt{A^2+B^2+2AB\cos\theta}$$

$$V=\sqrt{V_x^2+V_y^2+2V_xV_y\cos\theta}$$

$$=\sqrt{2V_x^2+2V_x^2\cos\theta}$$

$$=\sqrt{2V_x^2(1+\cos\theta)}$$

$$=V_x\sqrt{2 \cdot 2\cos^2(\frac{\theta}{2})}$$

$$=2V_x\cos\frac{\theta}{2}$$

$$2\cos^{-1}\frac{V}{2V_x}=\theta$$

Somehow, I took ##V=V_x## cause, I couldn't get any other way to remove them. When I took ##V=V_x## then, I got ##\theta=120 \deg##. But, which was completely wrong. The answer was ##45 \deg##. I was trying to use another equation. ##\vec A \cdot \vec B=AB\cos\theta##; Using the equation I got ##0## which is 100% wrong.