Questions

A 2-m wide truck is moving with a uniform speed v_{0} = 8 ms^{-1} along a straight horizontal road. A pedestrian starts to cross the road with a uniform speed v when the truck is 4 m away from him. The minimum value of v so that he can cross the road safely is

60 mins Expert Faculty Ask Questions

a

2.62 ms-1

b

4.6 ms-1

c

3.57 ms-1

d

1.414 ms-1

detailed solution

Correct option is C

Let the man start crossing the road at an angle 0 with the roadside. For safe crossing, the condition is that the man must cross the road by the time the truck describes the distance (4 + 2 cot θ) 4+2cotθ8=2/sinθv or v=82sinθ+cosθ For minimum v,dvdθ=0 -8(2cosθ-sinθ)(2sinθ+cosθ)2=0 or 2cosθ-sinθ=0 tanθ=2, so sinθ=25,cosθ=15 vmin=8225+15=85=3.57 ms-1

Similar Questions

The driver of a car moving towards a rocket launching with a speed of 6 ms^{-1} observed that the rocket is moving with speed of 10 ms^{-1}.The upward speed of the rocket as seen by the stationary observer is nearly

799 666 8865

support@infinitylearn.com

6th Floor, NCC Building, Durgamma Cheruvu Road, Vittal Rao Nagar, HITEC City, Hyderabad, Telangana 500081.

JEE

JEE Mock Tests

JEE study guide

JEE Revision Notes

JEE Important Questions

JEE Sample Papers

JEE Previous Year's Papers

NEET

NEET previous year’s papers

NEET important questions

NEET sample papers

NEET revision notes

NEET study guide

NEET mock tests

Popular Books

HC Verma Part 1HC Verma Part 2RS AgarwalRD SharmaLakhmir SinghDK GoelSandeep GargTS GrewalNCERT solutions

Class 12 NCERT SolutionsClass 11 NCERT SolutionsClass 10 NCERT SolutionsClass 9 NCERT SolutionsClass 8 NCERT SolutionsClass 7 NCERT SolutionsClass 6 NCERT Solutions