A car 2 m wide is parked along the edge of a road. At the instant, the car is started, a boy standing 6 m ahead of the car begins to cross the road with constant speed vs. If the acceleration of the car 1.5 ms-2 and if it continues to move along the edge, then the minimum value of v0=(n)12ms−1 for which boy can avoid collide. The value of n is ____

Here, t=dv0sin⁡θ=2v0sin⁡θ and 6+v0tcos⁡θ=12at2⇒ 6+v0tcos⁡θ=1.52t2⇒ 6+v0cos⁡θ2v0sin⁡θ=1.522v0sin⁡θ2⇒ 6+2cot⁡θ=36+2cot⁡θ⇒ v02sin2⁡θ=36+2cot⁡θ⇒ v02=3(6+2cot⁡θ)sin2⁡θFor minimum value of v02,y=(6+2cot⁡θ)sin2⁡θ should be maximum. ∴     dydθ=12sin⁡θcos⁡θ+2cos⁡2θ    6sin⁡2θ+2cos⁡2θ=0 Or      tan⁡2θ=−26=−13∴     v0min2=36sin2⁡θ+sin⁡2θPutting the value of θ,v0min2=8⇒v0min=8ms−1∴ n=8