A man walks 15m north then 20m at 32° E of N and then 11 m at at 15° S of W determine his net displacement
To determine the net displacement of the man, we can break down his movements into horizontal and vertical components.
First, let's calculate the horizontal displacement:
The man walks 20m at 32° E of N, which means he moves towards the east in the north-east direction. The horizontal component can be found using the formula:
Horizontal displacement = distance * cos(angle)
In this case, the distance is 20m and the angle is 32°. Plugging these values into the formula, we get:
Horizontal displacement = 20m * cos(32°)
Horizontal displacement ≈ 16.98m (rounded to two decimal places)
Next, let's calculate the vertical displacement:
The man walks 15m north and then 11m at 15° S of W, which means he moves towards the south in the north-west direction. The vertical component can be found using the formula:
Vertical displacement = distance * sin(angle)
For the first part, walking 15m north, the vertical displacement will be 15m because he is moving directly north, and there is no angle to consider.
For the second part, he walks 11m at 15° S of W. Since the angle is south of west (opposite direction of positive y-axis), we consider it as a negative angle. Plugging the values into the formula, we get:
Vertical displacement = 11m * sin(-15°)
Vertical displacement ≈ -2.90m (rounded to two decimal places)
Finally, we can find the net displacement by combining the horizontal and vertical displacements:
Net displacement = √(Horizontal displacement^2 + Vertical displacement^2)
Plugging the values we calculated earlier, we get:
Net displacement ≈ √((16.98m)^2 + (-2.90m)^2)
Net displacement ≈ √(288.8004m^2 + 8.41m^2)
Net displacement ≈ √297.2104m^2
Net displacement ≈ 17.23m (rounded to two decimal places)
Therefore, the man's net displacement is approximately 17.23 meters.