Kinematics Question 587
Question: The x and y components of $ \overrightarrow{\text{A}} $ are 4 m and 6 m, respectively. The x and y components of $ (\overrightarrow{A}+\overrightarrow{B}) $ are 10 m and 9 m respectively. The magnitude of vector b is:
Options:
A) 19 m
B)$ \sqrt{27} $
C) $ \sqrt{45} $
D)$ \sqrt{50} $
Show Answer
Answer:
Correct Answer: C
Solution:
[c] $ \vec{A} = 4\hat{i}+6\hat{j}$.
If $ {{\text{B}} _{\text{x}}} $ and $ {{\text{B}} _{\text{y}}} $ are the components of vector along x and y axes, then $ \text{4+}{{B _{x}}\text{=10, }}\therefore {{B _{x}}=6} $ Also $ \text{6+}{{B _{y}}}\text{=9, }\therefore {{B _{y}}=3}. $
$ \text{Thus, B}\text{=}\sqrt{\text{B} _{x}^{2}\text{+B} _{y}^{2}}=\sqrt{6^{2}+3^{2}}=\sqrt{45}. $
