On the way to class, you walk north and then west such that your resultant displacement is 290 m in a direction 250 west of north. Your average velocity is 2.0 m/s in the same direction as the displacement. Calculate (a) your walking time and (b) your average speed.

Direction = 25.0o West of north?

a. D = 290m[25.0o]

t = D/V = 290[25.0]/2[25o] = 145 s.

b. r = D/t = 290m/145s = 2m/s.

To solve this problem, we can use the concepts of vector addition and average velocity.

Let's start with finding the time it takes to walk to class.

(a) Calculate walking time:
To find the walking time, we need to know the magnitude of the displacement and the average velocity.

The magnitude of the displacement is given as 290 m, and the direction of the displacement is 250 degrees west of north.

To find the walking time, we divide the magnitude of the displacement by the average velocity:

Walking time = Displacement / Average velocity

We can break down the displacement into its north and west components:
Displacement (north) = 290 m * sin(250 degrees)
Displacement (west) = 290 m * cos(250 degrees)

Let's calculate:

Displacement (north) = 290 m * sin(250 degrees) ≈ -208.43 m
Displacement (west) = 290 m * cos(250 degrees) ≈ -195.45 m

Now we can calculate the north and west components of the average velocity:
Average velocity (north) = 2.0 m/s * sin(250 degrees)
Average velocity (west) = 2.0 m/s * cos(250 degrees)

Let's calculate:

Average velocity (north) = 2.0 m/s * sin(250 degrees) ≈ -1.43 m/s
Average velocity (west) = 2.0 m/s * cos(250 degrees) ≈ 1.34 m/s

Next, we divide the north component of the displacement by the north component of the average velocity to get the walking time:

Walking time = Displacement (north) / Average velocity (north)

Walking time = (-208.43 m) / (-1.43 m/s) ≈ 145.73 s

Therefore, the walking time is approximately 145.73 seconds.

(b) Calculate average speed:
Average speed is the total distance traveled divided by the total time taken.

Total distance traveled is the magnitude of the displacement, which is given as 290 m.

To find the average speed, we divide the total distance traveled by the walking time:

Average speed = Total distance traveled / Walking time

Average speed = 290 m / 145.73 s ≈ 1.99 m/s

Therefore, the average speed is approximately 1.99 m/s.