What is the magnitude of your total displacement if you have traveled due west with a speed of 23 m/s for 125 s , then due south at 12 m/s for 255 s ? 2sf
What is the direction of your total displacement in part A.
To find the magnitude of the total displacement, we can use the Pythagorean theorem. Since the motion is in two perpendicular directions (west and south), we can treat them as the legs of a right triangle.
Step 1: Calculate the displacement in the west direction.
The speed is given as 23 m/s, and you traveled for 125 seconds. So, the displacement in the west direction can be calculated using the formula: displacement = speed * time.
Displacement in the west direction = 23 m/s * 125 s = 2875 m west.
Step 2: Calculate the displacement in the south direction.
The speed is given as 12 m/s, and you traveled for 255 seconds. So, the displacement in the south direction can be calculated using the formula: displacement = speed * time.
Displacement in the south direction = 12 m/s * 255 s = 3060 m south.
Step 3: Calculate the magnitude of the total displacement.
Using the Pythagorean theorem, the magnitude of the total displacement can be found as the square root of the sum of the squares of each displacement.
Magnitude of total displacement = √((2875 m)^2 + (3060 m)^2) = √(8275625 m^2 + 9363600 m^2) = √(17669225 m^2) ≈ 4202.58 m (rounded to 2 significant figures).
Therefore, the magnitude of the total displacement is approximately 4202.58 m.
To determine the direction of the total displacement, we can use the tangent function and calculate the angle of the displacement relative to the positive x-axis (east).
Step 4: Calculate the angle of the total displacement.
Using the inverse tangent function, the angle can be calculated as: angle = arctan(y / x), where y is the displacement in the south direction and x is the displacement in the west direction.
Angle = arctan(3060 m / 2875 m) ≈ 46.78 degrees.
Therefore, the direction of the total displacement is approximately 46.78 degrees south of west.
A. X = -23*125 = -2875 m.
Y = -12*255 = -3060i.
Disp. = sqrt(x^2+y^2).
B. Tan A = Y/X. A = ?. = Direction.