a jogger runs with a veloicty of 6km/h (25 degrees N of W) for 35 min and then changes direction, Jogging for 20 min at 4.5km/h (65 degrees E of N). Using the parallelogram method for vector addition, determine the joggers total displacement and his average velocity for his workout

this questions stupid

To solve this problem using the parallelogram method for vector addition, we will break down the jogger's motion into two components: one in the north-south direction and the other in the east-west direction.

Step 1: Convert the velocities to their vector form. Velocity is a vector quantity and has both magnitude and direction. The jogger's velocity of 6 km/h (25 degrees N of W) can be represented as:
v1 = 6 km/h (25° N of W)

Similarly, the velocity of 4.5 km/h (65 degrees E of N) can be represented as:
v2 = 4.5 km/h (65° E of N)

Step 2: Resolve the vectors into their north-south and east-west components. To do this, we will use trigonometry.

For v1:
North-South component v1 (NS) = 6 km/h * sin(25°) = 2.572 km/h (positive north direction)
East-West component v1 (EW) = 6 km/h * cos(25°) = 5.437 km/h (negative west direction)

For v2:
North-South component v2 (NS) = 4.5 km/h * sin(65°) = 3.906 km/h (positive north direction)
East-West component v2 (EW) = 4.5 km/h * cos(65°) = 1.873 km/h (positive east direction)

Step 3: Find the resultant displacement. The resultant displacement is the sum of the north-south and east-west components.

North-South displacement = v1 (NS) * time1 + v2 (NS) * time2
= 2.572 km/h * (35 min/60 min/h) + 3.906 km/h * (20 min/60 min/h)
= 1.498 km + 1.302 km
= 2.800 km (positive north direction)

East-West displacement = v1 (EW) * time1 + v2 (EW) * time2
= 5.437 km/h * (35 min/60 min/h) + 1.873 km/h * (20 min/60 min/h)
= 3.176 km + 0.625 km
= 3.801 km (positive east direction)

The resultant displacement is the vector sum of the north-south and east-west displacements:
Resultant displacement = √(North-South displacement)^2 + (East-West displacement)^2
= √(2.800 km)^2 + (3.801 km)^2
= √7.84 km^2 + 14.448 km^2
= √22.288 km^2
≈ 4.72 km

Step 4: Find the average velocity. The average velocity is the total displacement divided by the total time taken.

Total displacement = resultant displacement = 4.72 km (in an unknown direction)
Total time = time1 + time2 = 35 min + 20 min = 55 min = (55/60) hours

Average velocity = Total displacement / Total time
= 4.72 km / (55/60) hours
= 5.155 km/h (approximately) in the direction of the resultant displacement.

Therefore, the jogger's total displacement is approximately 4.72 km, and his average velocity for the workout is approximately 5.155 km/h in the direction of the resultant displacement.

To determine the jogger's total displacement and average velocity, we need to break down the given displacements into their x and y components, add them up using the parallelogram method, and then calculate the magnitude and direction of the resultant vector.

First, let's break down the given displacements into their x and y components.

For the first part, with a velocity of 6 km/h at 25 degrees N of W, we have:
Velocity = 6 km/h
Angle = 25 degrees

To find the x and y components, we can use the following formulas:
x-component = Velocity * cos(Angle)
y-component = Velocity * sin(Angle)

For the first part, the x-component is:
x1 = 6 km/h * cos(25 degrees)
x1 ≈ 5.470 km/h

The y-component is:
y1 = 6 km/h * sin(25 degrees)
y1 ≈ 2.578 km/h

For the second part, with a velocity of 4.5 km/h at 65 degrees E of N, we have:
Velocity = 4.5 km/h
Angle = 65 degrees

The x-component is:
x2 = 4.5 km/h * sin(65 degrees)
x2 ≈ 3.838 km/h

The y-component is:
y2 = 4.5 km/h * cos(65 degrees)
y2 ≈ 1.877 km/h

Now, we can add up the x and y components using the parallelogram method.

x_total = x1 + x2
x_total ≈ 5.470 km/h + 3.838 km/h
x_total ≈ 9.308 km/h

y_total = y1 + y2
y_total ≈ 2.578 km/h + 1.877 km/h
y_total ≈ 4.455 km/h

The total displacement is given by the resultant vector, which is the diagonal of the parallelogram formed by the x and y components.

magnitude = sqrt(x_total^2 + y_total^2)
magnitude ≈ sqrt((9.308 km/h)^2 + (4.455 km/h)^2)
magnitude ≈ sqrt(86.687 km^2/h^2)
magnitude ≈ 9.321 km/h

The direction can be determined by taking the inverse tangent of the y and x components.

direction = atan(y_total / x_total)
direction ≈ atan(4.455 km/h / 9.308 km/h)
direction ≈ 26.9 degrees

Therefore, the jogger's total displacement is approximately 9.321 km/h at an angle of 26.9 degrees.

To calculate the average velocity, we divide the total displacement by the total time.

Total time = 35 min + 20 min
Total time = 55 min

Average velocity = Total displacement / Total time
Average velocity ≈ 9.321 km/h / (55 min / 60 min/h)
Average velocity ≈ 10.145 km/h

Therefore, the jogger's average velocity for the workout is approximately 10.145 km/h.