BITSAT 2015 Paper

Let the man starts crossing the road at an angle θ as shown in figure. For safe crossing the condition is that the man must cross the road by the time the truck describes the distance 4 + AC or 4 + 2cot θ
∴

4+2cotθ

8

=

2∕sinθ

v

or v =

8

2sinθ+cosθ

... (i)
For minimum v ,

dv

dθ

= 0

or

−8(2cosθ−sinθ)

(2sinθ+cosθ)2

= 0 or 2 cos θ - sin t = 0
or tan θ = 2
From equation (i),
vmin =

8

2( 2 √5 )+ 1 √5

=

8

√5

= 3.57 m/s