What is the shortest distance from his starting point?
Understanding the Walking Path
This problem involves finding the shortest distance between the starting point and the final point after a series of movements. This is also known as calculating the displacement. Let's break down the man's journey step by step:
- The man starts at a certain point.
- He walks 4 km North.
- He turns right (which means he now faces East) and walks 3 km.
- He turns right again (which means he now faces South) and walks 4 km.
Calculating the Net Displacement
We can visualize this path on a coordinate plane. Assume the starting point is the origin (0,0).
- Step 1: 4 km North
- The man moves from (0,0) to (0, 4). His position is now 4 km North of the start.
- Step 2: Turns right (East) and walks 3 km
- From (0, 4), he moves 3 km East. His new position is (0+3, 4) which is (3, 4).
- Step 3: Turns right again (South) and walks 4 km
- From (3, 4), he moves 4 km South. His final position is (3, 4-4) which is (3, 0).
Determining the Shortest Distance
The starting point was (0,0) and the final point is (3,0).
The shortest distance is the straight-line distance between these two points. We can use the distance formula, which is derived from the Pythagorean theorem:
Distance \(= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Here, \((x_1, y_1) = (0,0)\) and \((x_2, y_2) = (3,0)\).
Plugging in the values:
Distance \(= \sqrt{(3 - 0)^2 + (0 - 0)^2}\)
Distance \(= \sqrt{(3)^2 + (0)^2}\)
Distance \(= \sqrt{9 + 0}\)
Distance \(= \sqrt{9}\)
Distance \(= 3\) km
Final Answer
The shortest distance from his starting point is 3 km. This means the man ends up 3 km East of where he started.
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Important Questions from Direction and Distance
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According to the time by Rick's watch its quarter past eight. If the minute hand points towards the east, towards which direction would the hour hand point?
