Question

V = 15(cos60°i + sin60°j)

u = 25(cos30°i + sin30°j)
Find the magnitude of the sum of v and u. Round to the nearest hundredth.
A) 6.32
B) 7.39
C) 33.32
D) 38.72

Answer 1

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

Answer 2

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