Two hikers set off from the same point at 12:00 pm. The first walks N20°E at a speed of 67 m/min and after three hours reaches a cabin. The second walks N50°W at a speed of 83m/min. Determine the distance between the hikers at 3 pm?
To find the distance between the hikers at 3 pm, we need to determine the position of each hiker at that time.
First, let's find the position of the first hiker who walks N20°E at a speed of 67 m/min. Since they walk for three hours, the distance covered by this hiker can be calculated as follows:
Distance1 = Speed × Time
Distance1 = 67 m/min × 3 hours
To calculate the distance covered by the first hiker, we need to convert the time from hours to minutes:
Distance1 = 67 m/min × 3 hours × 60 min/hour
Next, we need to find the position of the second hiker who walks N50°W at a speed of 83 m/min. Again, since they walk for three hours, the distance covered by this hiker can be calculated as follows:
Distance2 = Speed × Time
Distance2 = 83 m/min × 3 hours
Similarly, to calculate the distance covered by the second hiker, we need to convert the time from hours to minutes:
Distance2 = 83 m/min × 3 hours × 60 min/hour
To determine the position of each hiker, we can use trigonometry to break down the distances into north-south and east-west components.
For the first hiker:
North-South distance1 = Distance1 × sin(20°)
East-West distance1 = Distance1 × cos(20°)
For the second hiker:
North-South distance2 = Distance2 × sin(50°)
East-West distance2 = Distance2 × cos(50°)
Now, we can find the distance between the hikers by calculating the Euclidean distance between their respective positions:
Distance between hikers = √((North-South distance2 - North-South distance1)^2 + (East-West distance2 - East-West distance1)^2)
By substituting the appropriate values into the formula, we can determine the distance between the hikers at 3 pm.