Question

a 2m wide truck us moving with a speed of 5√5m/s along a straight horizontal road a man starts crossing the road with a uniform speed v when the truck is 4m away from him. the minimum value of v (in m/s) to cross the truck saftely​

Answer 1

Answer:

HOPE IT HELP ;)

Explanation:

Let the man start crossing the road at an angle θ with the road side. For safe crossing, the condition is that the man must cross the road by the time, the truck describes the distance (4+2cosθ).

So,

2

4+2cotθ

=

v

2/sinθ

or v=

2sinθ+cosθ

2

For minimum v,

dθ

dv

=0

⇒

(2sinθ+cosθ)

2

−2(2cosθ−sinθ)

=0

⇒2cosθ−sinθ=0

⇒tanθ=2,so sinθ=

5

2

,cosθ=

5

1

v

min

=

2(2/

5

)+(1/

5

)

2

=

5

2

5

=0.89 m/s.

Answer 2

for both the vehicles the time is same so equate time on both the sides

t=distance/velocity

4/5√5=2/v now cross multiply

10√5/4=v

5.59

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