- #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.
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}##
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}##