Question

Find out the magnitude of resultant of two displacement vectors, each having a y-component of 10 km, are added together to form a resultant that forms an angle of 60${}^o$ from the +x-axis. (sin 60${}^o$= 0.87, cos 60${}^o$ = 0.5)

• A. 23 m
• B. 40 m
• C. 12 m
• D. 20 m
• E. 30 m

Answer 1

Answer: (A)

23 m

$\overrightarrow{A}=x_1\hat{i}+10\hat{j}\overrightarrow{B}=x_2\hat{i}+10\hat{j}\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{A}=(x_1+x_2)\hat{i}+20\hat{j}\Rightarrow \frac{20}{x_1+x_2}=tan{60}^0=\frac{0.87}{0.5}\Rightarrow x_1+x_2=\frac{10}{0.87}\Rightarrow |\overrightarrow{A}+\overrightarrow{B}|=\sqrt{{\left(\frac{10}{.87}\right)}^2+{20}^2}=23km$