Question

What is the magnitude of your total displacement if you have traveled due west with a speed of 23 m/s for 165 s, then due south at 12 m/s for 235 s?

Answer 1

The magnitude of the total displacement is 4725 meters.

Step-by-step explanation:

To find the magnitude of the total displacement, we need to calculate the individual displacements in both the west and south directions and then find the vector sum of these displacements.

Given:

• Speed due west = 23 m/s; Time due west = 165 s
• Speed due south = 12 m/s; Time due south = 235 s

Calculating the west displacement:

Distance = Speed x Time = 23 m/s x 165 s = 3795 m

Calculating the south displacement:

Distance = Speed x Time = 12 m/s x 235 s = 2820 m

To find the magnitude of the total displacement, we can use the Pythagorean theorem:

Displacement = sqrt((West Displacement)^2 + (South Displacement)^2) = sqrt(3795^2 + 2820^2) = sqrt(14364025 + 7952400) = sqrt(22316425) = 4725 m

Therefore, the magnitude of the total displacement is 4725 meters.