The resultant of Vectors having 3.0m/s, 45 deg and 5.0m/s, 135 deg is [tex]|r|=\sqrt{34} \mathrm{m} / \mathrm{s}[/tex].
Explanation:
We have , two vectors with specified direction and magnitude. A vector is a quantity which has both magnitude & direction. Vector 1 has magnitude of 3 and direction of 45° whereas vector 2 has magnitude of 5 and direction of 135°.
∴ Resultant of both vectors is :
r = a + b
Resultant angle between two vectors is : 135°- 45° = 90°, cos90°=0
⇒[tex]a=|3| \times(i \sin \theta+j \cos \theta)\\b=|5| \times(i \sin \theta+j \cos \theta)\\\\\begin{array}{c}r=a+b \\\\|r|=\sqrt{|a|^{2}+|b|^{2}+2|a| \times|b| \cos \theta}\end{array}\\\\|r|=\sqrt{|3|^{2}+|5|^{2}+2 \times|3| \times|5| \cos 90^{\circ}}\\[/tex]
[tex]|r|=\sqrt{34}[/tex]
∴ Resultant of above two vectors is [tex]|r|=\sqrt{34} \mathrm{m} / \mathrm{s}[/tex].
