- #1

Benjamin_harsh

- 211

- 5

- Homework Statement
- Find the resultant vector of vectors A and B shown in the figure.

- Relevant Equations
- ##\large \frac {R}{Sin 70^0} = \frac {17}{Sin\alpha}##

Find the resultant vector of vectors A and B shown in the figure.

By geometry method:

Cosine law for the right side triangle.

##R^{2} = 17^{2} + 44^{2} - 2 (17)(14).cos 70^{0}##

##R = 41.39 m/sec##

By Sin law,

##\large\frac {R}{Sin 70^0} = \frac {17}{Sin\alpha}##

##sin \alpha = \large \frac{17.sin 70^{0}}{R} = \frac{17.sin 70^{0}}{41.39}##

##\alpha = 22.70^{0}##

##\theta_{x} = 50 + \alpha = 50 + 22.70##

##\theta_{x} = 72.70^{0}##

**Solution**:By geometry method:

Cosine law for the right side triangle.

##R^{2} = 17^{2} + 44^{2} - 2 (17)(14).cos 70^{0}##

##R = 41.39 m/sec##

By Sin law,

##\large\frac {R}{Sin 70^0} = \frac {17}{Sin\alpha}##

##sin \alpha = \large \frac{17.sin 70^{0}}{R} = \frac{17.sin 70^{0}}{41.39}##

##\alpha = 22.70^{0}##

##\theta_{x} = 50 + \alpha = 50 + 22.70##

##\theta_{x} = 72.70^{0}##