"A jogger runs with a velocity of 6.0 km/h [25° N of W] for 35 min and then changes direction, jogging for 20 min at 4.5 km/h [65° E of N]. Using a vector diagram, determine the jogger's total displacement and his average velocity for the workout."

I know the answer, what I would appreciate is knowing how to get. Because it doesn't happen in the same amount of time I know I cannot use x/y components and I'm unsure of what else to do. Any help would be appreciated, thank you.

Well, figuring this out might take a bit of jogging your memory, but I'll do my best to help you!

To determine the jogger's total displacement, we can break down the problem into two parts - one for each leg of the jog.

For the first part, where the jogger runs for 35 minutes at 6.0 km/h [25° N of W], we can find the displacement using trigonometry. The jogger is going in the northwest direction, so we can think of this as moving in two perpendicular directions - north and west.

The northward component can be calculated as:
displacement_north = velocity * time * sin(angle)
= 6.0 km/h * (35 min / 60 min/h) * sin(25°)

Similarly, the westward component can be calculated as:
displacement_west = velocity * time * cos(angle)
= 6.0 km/h * (35 min / 60 min/h) * cos(25°)

Now, we can find the total displacement for the first leg of the jog by using the Pythagorean theorem:
displacement_1 = sqrt(displacement_north^2 + displacement_west^2)

For the second part of the jog, where the jogger runs for 20 minutes at 4.5 km/h [65° E of N], the calculation follows a similar process. The northward component is found using sin(65°) and the eastward component using cos(65°).

Now, to find the total displacement for the entire jog, we can treat the displacement of the first and second parts as vectors and add them together. You can do this by creating a vector diagram and simply adding the two vectors together.

As for the average velocity, that can be found by dividing the total displacement by the total time taken for the entire jog. You'll just need to convert the time into hours before performing the calculation.

So, by following these steps, you should be able to figure out the jogger's total displacement and average velocity. Enjoy your jog of knowledge!

To determine the jogger's total displacement and average velocity, you can follow these steps:

Step 1: Convert the given velocities from km/h to m/s.

- The first velocity is 6.0 km/h [25° N of W]. Convert it to m/s:

6.0 km/h = (6.0 * 1000) / (60 * 60) m/s = 1.67 m/s

- The second velocity is 4.5 km/h [65° E of N]. Convert it to m/s:

4.5 km/h = (4.5 * 1000) / (60 * 60) m/s = 1.25 m/s

Step 2: Find the displacement for each leg of the jog using the formula:
Displacement = Velocity x Time

- For the first leg of the jog (25° N of W), the velocity is 1.67 m/s and the time is 35 minutes. Convert the time to seconds:

35 minutes = 35 * 60 seconds = 2100 seconds

So, the displacement for the first leg is:

Displacement1 = 1.67 m/s x 2100 seconds = 3507 m

- For the second leg of the jog (65° E of N), the velocity is 1.25 m/s and the time is 20 minutes. Convert the time to seconds:

20 minutes = 20 * 60 seconds = 1200 seconds

So, the displacement for the second leg is:

Displacement2 = 1.25 m/s x 1200 seconds = 1500 m

Step 3: Use vector addition to find the total displacement.

- Draw a vector diagram showing the first and second displacements as vectors originating from the same point.
- Add these vectors graphically using the head-to-tail method.
- Measure the length of the resultant vector using a ruler.
- Convert the measured length back to km.

Let's assume the length of the resultant vector on the diagram is 5 cm. If the scale is 1 cm = 1000 m, then the length of the resultant vector is:

Length of Resultant Vector = 5 cm x 1000 m/cm = 5000 m = 5 km

So, the total displacement of the jogger is 5 km.

Step 4: Calculate the average velocity of the jogger.

- Average velocity is the total displacement divided by the total time taken.

Total time taken = 35 minutes + 20 minutes = 55 minutes = 55 * 60 seconds = 3300 seconds

Average velocity = Total Displacement / Total Time Taken

Average velocity = 5 km / 3300 seconds

Average velocity ≈ 0.0015 km/s

Therefore, the jogger's total displacement is 5 km, and their average velocity for the workout is approximately 0.0015 km/s.

To find the jogger's total displacement and average velocity, we can break down the jogger's motion into two components: the north-south (vertical) component and the east-west (horizontal) component.

1. Breaking down the first leg of the jog:
The jogger runs with a velocity of 6.0 km/h [25° N of W] for 35 minutes. We can break this velocity into north-south and east-west components, using trigonometry:
- The north-south component of velocity = 6.0 km/h * sin(25°)
- The east-west component of velocity = 6.0 km/h * cos(25°)
Now, since the jogger runs for 35 minutes, we need to convert this time to hours by dividing it by 60. Let's call this time as t1.

2. Breaking down the second leg of the jog:
The jogger changes direction and runs at 4.5 km/h [65° E of N] for 20 minutes. Similar to step 1, we can find the north-south and east-west components of velocity using trigonometry:
- The north-south component of velocity = 4.5 km/h * cos(65°)
- The east-west component of velocity = 4.5 km/h * sin(65°)
Again, convert the time of 20 minutes into hours by dividing it by 60. Let's call this time as t2.

3. Total displacement:
To find the total displacement of the jogger, we need to consider both components of motion. Add up both the north-south and east-west components of displacement:
- North-south displacement = (north-south component of velocity for t1 * t1) + (north-south component of velocity for t2 * t2)
- East-west displacement = (east-west component of velocity for t1 * t1) + (east-west component of velocity for t2 * t2)
The total displacement is the vector sum of these two displacements.

4. Average velocity:
To find the average velocity, we need to divide the total displacement by the total time taken for the entire jog, which is t1 + t2.
- Average velocity = Total displacement / (t1 + t2)

By following these steps and using the given information, you will be able to determine the jogger's total displacement and average velocity for the workout.

work in distances: distance=speed*time

then add the x,y compnents of distances