Question

V = 15(cos60°i + sin60°j)

Answer 1

1. $cos60^{0}=sin30^{0}=0.5 \\ sin60^{0}=cos30^{0}= \frac{ \sqrt{3}}{2}$
2. v+u=$(15cos60^{0}+25cos30^{0})i+(15sin60^{0}+25sin30^{0})j$
3. v+u=$(7.5+12.5 \sqrt{3} )i+(7.5 \sqrt{3} +12.5)j$
4. The magnitude of the sum u+v is $\sqrt{(7.5+12.5 \sqrt{3} )^{2}+(7.5 \sqrt{3} +12.5)^2}$=38.72
Answer: D is correct choice

Answer 2

As,
v=15(cos60°i + sin60°j)
u=25(cos30°i + sin30°j)
We know that
cos60°=sin30°=0.5
sin60°=cos30°=√3/2

v+u=15(0.5i+√3/2j)+25(√3/2i+0.5j)
v+u=(29.15i+25.49j)
|v+u|=√(29.15)²+(25.49)²
        =38.72

Option D is correct