Die runs 200 meters north, 500 meters west, and finally 150 meters at 30 degrees north of east. What is her total displacement?
North = 200 + 150 sin 30
West = 500 - 150 cos 30
North = 200 + 75 = 275
West = 500 - 130 = 370
distance = sqrt (275^2 + 370^2)
angle north of west = arc tan (275/370)
Thank you! That was very helpful.
To find the total displacement, we need to determine the net distance and direction from the starting point to the ending point.
Let's break down the given information:
- Die runs 200 meters north
- Die runs 500 meters west
- Die runs 150 meters at 30 degrees north of east
First, let's calculate the westward and eastward components of the displacement.
Westward displacement:
Since Die runs 500 meters west, the westward component of the displacement is -500 meters (negative sign indicates westward direction).
Eastward displacement:
To calculate the eastward displacement, we need to find the horizontal component of the 150 meters displacement at 30 degrees north of east. The formula to find the horizontal component is:
Horizontal displacement = Displacement * cos(angle)
Using this formula:
Horizontal displacement = 150 meters * cos(30 degrees) = 150 meters * √3/2 ≈ 129.90 meters (rounded to two decimal places)
Now, let's calculate the northward component of the displacement.
Northward displacement:
Since Die runs 200 meters north, the northward component of the displacement is +200 meters.
Next, let's find the net displacement by summing up the components.
Net displacement = (Horizontal displacement + Westward displacement) along the x-axis + Northward displacement along the y-axis
Net displacement = (129.90 meters - 500 meters) along the x-axis + 200 meters along the y-axis
Net displacement = -370.10 meters along the x-axis + 200 meters along the y-axis
Therefore, Die's total displacement is approximately 370.10 meters to the south of the starting point, considering the direction and magnitude.