Find the time between 2 and 3 when angle is 50 between hour and minute hands
Summary
TLDRIn this educational video, Anil Kumar introduces a strategy to solve problems involving the angle between clock hands. He presents a formula to calculate this angle and applies it to find the time between 2:00 and 3:00 PM where the angle is 50 degrees. The explanation covers two possible scenarios and uses the formula theta = |30H - 11/2M| to find two solutions: 2 hours and 20 minutes or approximately 2 hours and 1/9 of a minute. The video is designed to help viewers understand how to approach such problems and encourages them to engage with the content.
Takeaways
- ๐ The video discusses a method to find the angle between clock hands at a specific time.
- ๐ The specific question is to find the time between 2:00 and 3:00 PM where the angle is 50 degrees.
- ๐ Each hour on the clock represents an angle of 30 degrees, and each minute represents 6 degrees.
- ๐ค The presenter explains that there could be two solutions, one where the hour hand is ahead of the minute hand and another where it's behind.
- ๐ The formula to calculate the angle between the clock hands is given by theta = |30H - 11/2M|.
- ๐ For the given problem, H (hours) is between 2 and 3, and the angle theta is 50 degrees.
- ๐งฎ The presenter solves for M (minutes) using the formula and finds two possible times.
- ๐ The two solutions are approximately 2 hours and 20 minutes or 2 hours and 1/9 of a minute.
- ๐ A link is provided for the derivation of the formula used to calculate the angle.
- ๐ The presenter encourages viewers to comment, share, like, and subscribe for more content.
Q & A
What is the main topic of Anil Kumar's video series?
-The main topic of Anil Kumar's video series is strategies to solve questions, with a specific focus on finding the angle between clock hands.
What is the general formula provided to find the angle between clock hands?
-The general formula provided is theta equals 230 times H minus 11/2 times M, where H is the hour and M is the minutes.
What is the specific question Anil Kumar is trying to solve in the script?
-The specific question is to find the time between 2:00 and 3:00 p.m. where the angle between the hour and minute hand is 50 degrees.
How does Anil Kumar explain the angles on a clock?
-Anil Kumar explains that each position on the clock represents an angle of 30 degrees, starting from the 12 o'clock position.
What does Anil Kumar mean when he says there could be two solutions to the problem?
-Anil Kumar means that there could be two times within the hour where the angle between the clock hands is 50 degrees, one where the minute hand is ahead of the hour hand and another where it is behind.
What is the significance of the number 30 degrees in the context of the clock?
-The number 30 degrees signifies the angle between each hour mark on the clock face.
How does Anil Kumar use the formula to find the minutes (M) when the angle (theta) is 50 degrees?
-Anil Kumar uses the formula by substituting theta with 50 degrees and H with 2 hours, then solving for M in two scenarios: when the minute hand is ahead and when it is behind the hour hand.
What are the two possible times that Anil Kumar finds where the angle between the clock hands is 50 degrees?
-The two possible times are 2 hours and 20 minutes, and approximately 2 hours and 1/9 minutes.
What does Anil Kumar suggest at the end of the script for further understanding?
-Anil Kumar suggests that viewers look at the derivation of the formula for a deeper understanding of how the formula is derived.
How does Anil Kumar encourage viewer interaction at the end of the script?
-Anil Kumar encourages viewer interaction by inviting comments, asking viewers to share their views, and suggesting they like and subscribe to his videos.
Outlines
๐ Understanding Clock Angles
Anil Kumar introduces a series on problem-solving strategies, focusing on a question about the angle between clock hands. He explains the general formula to find the angle between the hour and minute hands of a clock. The specific question is to find the time between 2:00 and 3:00 PM where the angle between the hands is 50 degrees. Anil uses a visual representation of a clock to clarify how each position on the clock represents 30 degrees, leading to a full circle of 360 degrees. He discusses the two possible scenarios where the minute hand could be either ahead or behind the hour hand to achieve the 50-degree angle. The formula provided is theta = |30H - 11/2M|, where H is the hour and M is the minute, to calculate the angle.
๐ Solving for Time with Clock Angles
Anil Kumar continues the explanation by applying the formula to find the specific times between 2:00 and 3:00 PM where the angle is 50 degrees. He sets up two equations based on the formula, one where the minute hand is ahead and another where it is behind the hour hand. Solving these equations gives two possible times: 2 hours and 20 minutes or approximately 2 hours and 1/9 minutes (just shy of 2 minutes). Anil emphasizes that there are two solutions because the minute hand's position relative to the hour hand can vary. He concludes by offering a link for the derivation of the formula and encourages viewers to comment, share, and subscribe for more content.
Mindmap
Keywords
๐กAngle
๐กClock hands
๐กFormula
๐กDegrees
๐กHour hand
๐กMinute hand
๐กTime
๐กPosition
๐กSolve
๐กDerivation
๐กContext
Highlights
Introduction to solving the angle between clock hands.
Question posed: Find the time between 2:00 and 3:00 p.m. where the angle between hour and minute hands is 50 degrees.
Explanation of the clock face and angles between the numbers.
Each hour on the clock represents a 30-degree angle.
Understanding the position of the hour and minute hands between 2 and 3 o'clock.
Two possible scenarios where the angle could be 50 degrees.
The minute hand could be either ahead or behind the hour hand.
The formula to calculate the angle between the clock hands: theta = 230 * (H - (11/2) * M).
The angle is always positive, so the formula takes the absolute value.
Substituting the known values (H = 2, theta = 50 degrees) into the formula.
Two equations are derived from the formula to find the minutes (M).
Solving for the minutes gives two possible solutions.
The two solutions are 2 hours and 20 minutes or 2 hours and 1/9 of 11 minutes.
The importance of considering both the minute hand being ahead or behind the hour hand.
The final answer is presented: two hours and either 20 minutes or approximately 2 minutes and 1/9 of 11 minutes.
A link will be provided for the derivation of the formula used.
Encouragement for viewers to comment, share views, like, and subscribe.
Transcripts
I'm Anil Kumar welcome to my series on
strategies to solve questions here's a
very interesting question based on angle
between clock hands I'll provide you
with a general formula to find the angle
between clock hands and then solve this
particular question the question here is
find the time between 2:00 and 3:00 p.m.
where the angle between hour and minute
hand is 50 degrees
so let's first try to understand the
situation let's say we have a clock here
and we want the time between 2:00 to
3:00 p.m. when the angle between the two
hands is 50 degrees so let's say this is
1 for us this is 2 that is 3 4 5 6 7 8 9
10 11 and 112 so one position could be
so as well as the angles are concerned
let's be very clear about and they say
if this is zero then the the angle from
here to the center we can say this each
is actually 30 degrees right so each is
30 degrees so 30 is 60 90 120 150 180
and so on right so that is how the
angles are so within every hour there is
30 minutes now we are saying find the
time between 2 to 3 hours that means we
want a situation where the hour hand is
somewhere between these two and the
minute hand is 50 degrees away to say
that our hand let's say is let's say
here for example right let's say our
hand is here in that case minutes and is
50 away so 50 away means two are 60
right so somewhere some
like this do you understand so we
exactly don't know where but somewhere
like this correct right so we need to
find this position we don't know what
this question is but that angle should
be fifty degrees that's what we need
agree
well one more situation could be that
this arm is on the other side right so
that is to say we could also have this
somewhere here right and somewhere there
some some position between two two three
and we could also have an angle of 50
degrees between the two so when we say
that the angle is 50 degrees we are
actually looking for two solutions so in
one case the our hand is beyond
diminished and the other case which sand
is beyond the our hand you get an idea
correct now we also know from the speed
of our and the minutes hand that the
angle can be given by the formula theta
equals 230 times H minus 11 by 2 times 3
minutes and this angle is always
positive so we take a positive value
that is the absolute value of this right
so in our case we for sure know that H
is 2 hours between two so we will start
somewhere
more than 2 right but less than 3 so H s
2 we also know that theta is 50 degrees
using this formula we can write down 50
equals to absolute value 30 times 2
minus 11 over 2 minutes and then we can
find the minutes absolute value
basically means that we could solve for
two equations
all this inside all this inside could be
either positive 50 or negative 50 but
absolute value will be positive you get
the idea right so so we could write this
as 30 times 2 is 60 minus 1/2 of 2 M
equals 2 positive 50 or this could also
be 60 minus 11 by 2 M equals 2 minus 50
clear because absolute value of minus 50
is also 50 you get the idea right less
so so taking this to the right side we
get 60 minus 50 equals to 11 by 2 m and
that is 10 and then we'll multiply by 2
over 11 to get the value of M correct so
that is 20 by 11 which is 1 and 11 when
you take away you get 9 over 11 minutes
okay on this side we have 60 plus 15
equals to 11 over 2 M or we could say
110 times 2 over 11 equals to M and that
gives you M equals 2 this goes 10 times
M equals to 20 right so we have two
solutions here one of the time could be
to 20 right the other will be to 1/9 by
11 minutes right so slightly very close
to two minutes right so basically I
should write two hours and so many
minutes right so many minutes two hours
extra two hours and so many minutes is
that clear so it is two hours and 20
minutes in this case correct so that is
how you could actually solve this
question so that that should be I think
clear and straightforward now to look
into this I'll provide you with a link
- for the derivation of this formula how
do we get this formula as the angle
theta being equal to 30 times hours - 11
by 2 times minutes perfect but I hope
that helps you to understand that the
idea here is to find two different
solutions right
since the minutes arm could be before
hours or after hours of and then solve
it hope it makes sense feel free to
write your comment share your views and
if you like and subscribe to my videos
at P great thanks for watching and all
the best
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