An ant on a picnic table travels 40 cm eastward, then 25 cm northward, and finally 15 cm westward. What is the ant's directional displacement relative to its original position?
went 25 east and 25 north
25 sqrt(2) cm northeast
29cm
To find the ant's directional displacement, we need to consider the net displacement, which is the straight-line distance from the starting point to the ending point.
To solve this problem, we can use the Pythagorean theorem.
First, let's draw a diagram to visualize the ant's movements.
Starting from the original position, we move 40 cm eastward. This takes us 40 cm to the right. Now, we move 25 cm northward, which takes us 25 cm up. Finally, we move 15 cm westward, which takes us 15 cm to the left.
25 cm
B------------------ C
| |
| |40 cm
A------------------ D
15 cm
Let's label the points as follows:
- A: Original position
- B: Eastward position
- C: Final position
- D: Westward position
Now, we can calculate the net displacement using the Pythagorean theorem.
The horizontal displacement is the difference between points B and D, which is 40 cm - 15 cm = 25 cm.
The vertical displacement is the difference between points A and C, which is 25 cm.
Using the Pythagorean theorem, we can find the net displacement:
net displacement = √(horizontal displacement^2 + vertical displacement^2)
= √(25 cm^2 + 25 cm^2)
= √(625 cm^2 + 625 cm^2)
= √(1250 cm^2)
= √(1250) cm
≈ 35.36 cm
Therefore, the ant's directional displacement relative to its original position is approximately 35.36 cm.