IIT JEE , AIEEE Forum - Mathematics , Algebra

iamgodofdeath131

As we all know that the Hour hand and Minute hand on a clock travels at different speeds.However there are certain occasions when they are exactly opposite each other.Can you please drive formula for me to calculating the times of these occasions?

coolyog

wat do ya mean by xactly opposite each other

srujana

hello iamgodofdeath131

to answer such questions u have to find the relative speeds;

Angle made by the hours hand in 1 hour=360(degrees)/12(hrs)=30(degrees)

lly the angle made by the hours hand in 1 min = 1/2 degrees

the angle made by the minutes hand in 1 min = 360/60=6 degrees

hence the relative speed= 5 1/2 degrees per minute.

U make use of the formula TIME TAKEN BY THE TWO HANDS TO COVER x degrees = ANGLE COVERED/RELATIVE SPEED

srujana

SUPPOSE THEY GIVE U A Q....AT WHAT TIME BETWEEN 4 AND 5 HRS THE TWO HANDS OF A CLOCK ARE EXACTLY OPPOSITE TO EACH OTHER.....

Angle between the two hands at 4 hrs = 4*30=120

Angle required = 180

angle to be covered = 120 + 180 =300

therefore time taken= angle covered/speed(relative)

=300/5 1/2 = 54 4/11 min

therefore at 4 hrs 54 4/ 11 min, the two hands are exactly opposite to each other

amar.gupta

very good work srujana,

Dear iamgodofdeath131,

Let we start when there is exactly 12 o clock. i.e. 0 degree angle between them.

relative speed= [(2.pie/60) - 2.pie/(12*60) ] radian per minute

or = (2.pie/60)[1- (1/12)] radian per minute

or = (pie/30)[11/12] radian per minute

or = (11 pie/360) radians per minute

so time taken to cover pie radians = 360/11 minutes. = 6/11 hrs.

so after 6/11 hrs. they will be opposite to each other, and after that they will be opposite to each other when relative angle covered = 3* pie

so time taken = 18/11 hrs.

on generalisation: 6(2n-1)/11 where n=1,2,3,4............

so n=1, i.e. first time they will be opposite after 6/11 hrs from 12'0 clock.

so n=2, i.e. second time they will be opposite after 18/11 hrs from 12'0 clock.

so n=3, i.e. third time they will be opposite after 30/11 hrs from 12'0 clock.

and so on.........

srujana

Thank you sir

Ask & Discuss Questions with Community & Experts