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Namratha walks 14 metres towards west, then turns to her right and walks 14 meters and then turns to her left and walks 10 metres. Again turning to her left she walks 14 metres. What is the shortest distance (in metres) between her starting point and her present position?
- a)38m
- b)28m
- c)24m
- d)10m
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Namratha walks 14 metres towards west, then turns to her right and wal...
Let's break down Namratha's movements step by step:
- First Movement: She walks 14 meters west.
- Second Movement: She turns right and walks 14 meters north.
- Third Movement: She turns left and walks 10 meters west.
- Fourth Movement: She turns left again and walks 14 meters south.
Now, let's analyze her position.
- After the first movement, she's 14 meters west of the starting point.
- After the second movement, she's 14 meters west and 14 meters north of the starting point.
- After the third movement, she's 24 meters west and 14 meters north of the starting point.
- After the fourth movement, she moves 14 meters south, so she's now 24 meters west and at the same latitude as her starting point (because the south movement cancels out the north movement).
To find the shortest distance between her starting point and her present position, we just need to calculate the straight-line distance (which is the horizontal distance since her vertical displacement is zero).
Since she is 24 meters west of her starting point, the shortest distance is:
Distance=24 meters\text{Distance} = 24 \text{ meters}Distance=24 meters
So the correct answer is 24 meters (Option 3).
Most Upvoted Answer
Namratha walks 14 metres towards west, then turns to her right and wal...
Solution:
Let us draw the diagram as per the given information.
The shortest distance between her starting point and present position is the length of the hypotenuse of the right-angled triangle OPR.
Here,
OP = 14m (as she walks 14m towards west)
PR = 10m (as she walks 14m towards west, then turns left and walks 10m)
Using Pythagoras theorem,
Hypotenuse OR = √(OP² + PR²) = √(14² + 10²) = √(196 + 100) = √296 = 2√74
Hence, the shortest distance between her starting point and present position is 2√74 m.
Therefore, the correct answer is option C.
Let us draw the diagram as per the given information.
The shortest distance between her starting point and present position is the length of the hypotenuse of the right-angled triangle OPR.
Here,
OP = 14m (as she walks 14m towards west)
PR = 10m (as she walks 14m towards west, then turns left and walks 10m)
Using Pythagoras theorem,
Hypotenuse OR = √(OP² + PR²) = √(14² + 10²) = √(196 + 100) = √296 = 2√74
Hence, the shortest distance between her starting point and present position is 2√74 m.
Therefore, the correct answer is option C.
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