Question

please solve these question ..........please......​

Answer 1

Given,

A

=(coswt  

i

^

+sinw  

j

^

​  

)⋅

B

=(cos  

2

wt

​  

 

i

^

+sin  

2

wt

​  

 

j

^

​  

)

When they are orthogonal, their dot product will e zero

A

⋅  

B

=(coswt  

i

^

+sinwt  

j

^

​  

)⋅(cos  

2

wt

​  

 

i

^

+sin  

2

wt

​  

j)

0=cos(wt−  

2

wt

​  

)

cos(wt−  

2

wt

​  

)=0=  

2

π

​  

 

cos(  

2

wt

​  

)=  

2

π

​  

 

2

wt

​  

=  

2

π

​  

 

t=  

w

π

​  

 

Hence, value of time is  

ω

π

​

A=πR  

ma

2

​  

.....(1)

Maximum Range= R  

ma

​  

=  

g

v  

2

 

​  

............(2)

From (1) and (2) we get,

A=  

g  

2

 

πv  

4

 

​  

.

Answer 2

$\huge\underline{\overline{\mid{\bold{\red{ANSWER-}}\mid}}}$

Rmax = (v2/g) sin2θ = v2/g

Area = πR2 = πv4/g2

The correct option is C.