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` `1. A man wearing a hat of extende length 12 cm is running in rain falling vertically downwards with speed 10m/s.The maximum speed with which man can run,so that rain drops do not fall on his face (the length of his face below the extended part of the hat is 16 cm) will be?

2. A taxi leaves the station X for station Y every 10 min. Simultaneously ,a taxi also leaves the station Y for station X every 10 min. The taxis move at the same constant speed and go frm X to Y or vice versa in 2 hrs . How many taxis comin from the other will meet each taxi moving from X to Y/

7 years ago

(1)

let hz. vel. of man is:

Vm/secrain dropes fall at vt. velocity: 10m/sec

tan x = V/10 = 12/16

V

_{man}= 7.5 m/sec(2)

Let distance btn. X and Y be

S mtsand letVbe constant speed of carso

S=7200V(fom S=Vt relation )Since each car leave with 10 mins difference : gap btn. each car is s=V*600 = S*600/7200 = S/12

gap btn. each car is =

S/12mfollowing fig. explains it:

X -------S_{1}-------S_{2}-------S_{3}-------S_{4}-------S_{5}-------S_{6}-------S_{7}------S_{8}-------S_{9}-------S_{10}-------S_{11}-------Y

case 1:So, when cars start simultaneously from X and Ythen first cars from X and Y meet at

Sand will start to cross 6 taxis till reaching X(orY), so it'll meet a total of_{6}7 taxisincluding one at X(or Y)

case 2:after 10 mins from departure of 1st car from X(or Y) , a car starting from Y (orX) will meet a total of

8 taxisincluding one at X(or Y)the cases goes on till 2 hrs , and then a car from X(or Y) will meet a total of

13 taxisincluding one at X and Y.---

Since question

2isn't clear for me, I have given all possible cases.If u think , the answer is n't what u r looking for, plzz post the question clearly again .

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Regards,

Naga Ramesh

IIT Kgp - 2005 batch

7 years ago

Sir,

Sorry abt the wrong ques . The last line of the ques is:-

How many taxis coming from the other side will meet each taxi moving from Y to X?

7 years ago

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