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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/
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
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(1) let hz. vel. of man is: V m/sec rain 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 mts and let V be constant speed of car so 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/12 m following 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 Y then first cars from X and Y meet at S_{6} and will start to cross 6 taxis till reaching X(orY), so it'll meet a total of 7 taxis including 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 taxis including 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 taxis including one at X and Y. --- Since question 2 isn'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 . ---- Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
(1)
let hz. vel. of man is: V m/sec
rain 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 mts and let V be constant speed of car
so 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/12 m
following 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 Y
then first cars from X and Y meet at S_{6} and will start to cross 6 taxis till reaching X(orY), so it'll meet a total of 7 taxis including 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 taxis including 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 taxis including one at X and Y.
---
Since question 2 isn'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 .
----
Please feel free to post as many doubts on our disucssion forum as you can. If you find any question difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation. All the best. Regards, Naga Ramesh IIT Kgp - 2005 batch
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?
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?
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