Two vectors `vecA` and `vecB` are defined as `vecA=ahati` and `vecB=a( cos omegahati+sin omega hatj)`, were a is a constant and `omega=pi//6 rads^(-1)`. If `|vecA+vecB|=sqrt(3)|vecA-vecB|` at time `t=tau` for the first time, the value of `tau`, in seconds , is _________

Answer

4

Explanation

`R_(1)=u_(0) cos theta xx (2u_(0) sin theta)/(g)=R_(1)/alpha^(2), R_(2)=(u_(0))/(alpha) cos theta xx (2 u_(0) sin theta)/(alphag)=R_(1)/alpha^(2)`
`R_(3)=R_(1)/alpha^(4) rArr R_("Total")=R_(1)+R_(2)+R_(3)+........+(R_(1))/(1-1/alpha^(2))=(a^(2)R_(1))/(alpha^(2)-1) rArr T_(1)=(2u_(0) sin theta)/(g)`
`T_(2)=(2u_(0) sin theta)/(alpha g)=(T_(1))/(alpha) T_(3)=(T_(1))/(alpha^(2)) rArr T_("Total")=T_(1)+T_(2)+T_(3)+.....=(T_(1))/(1-1/alpha)=(alpha T_(1))/(alpha-1)`
`V_(1)=R_(1)/T_(1) and V_("avgentiemotion")=(R_("Total"))/(T_("Total"))=(alpha^(2)R_(1))/(alpha^(2)-1) xx (alpha-1)/(alpha+1) xx V_(1)=0.8 V_(1)`
`rArr =0.8 alpha+0.8 rArr 0.2alpha =0.8 rArr alpha=4`