A bus travels 80km due south in 2 hours.it then travels 100km due west in 3 hours.what is the average velocity of bus?
The average velocity of the bus is (80 km/2 h) + (100 km/3 h) = 66.67 km/h.
speed is a scalar
velocity is a vector (both magnitude AND DIRECTION)
V = -(100 * 10^3 meters / 180 seconds) i - (80*10^3 meters / 120 seconds) j
sorry 180 * 60 seconds and 120 * 60 seconds
( I assumed minutes not hours )
20
Well, let me do some calculations while making sure not to get tangled in traffic cones. To find the average velocity, we need to find the total displacement and divide it by the total time.
The bus traveled 80 km due south, so its displacement in the south direction is 80 km. It then traveled 100 km due west, so its displacement in the west direction is 100 km.
Now, let's calculate the average velocity. Since displacement is a vector quantity, we have to consider the direction as well.
The total displacement is the vector sum of the south and west displacements, which we can find using the Pythagorean theorem. The magnitude of the displacement is √(80^2 + 100^2) km ≈ 128.06 km.
The total time taken is the sum of the time taken in both directions, which is 2 hours + 3 hours = 5 hours.
Now, let's divide the total displacement (128.06 km) by the total time (5 hours):
Average velocity = total displacement / total time
Average velocity = 128.06 km / 5 hours
Average velocity ≈ 25.61 km/h
So, the average velocity of the bus is approximately 25.61 km/h. Just hope it's not late for the circus!
To find the average velocity of the bus, we need to calculate the total displacement and divide it by the total time taken.
The bus traveled 80 km due south in 2 hours, which means it had a displacement of -80 km in the south direction (negative sign indicates the south direction).
Next, the bus traveled 100 km due west in 3 hours, which means it had a displacement of -100 km in the west direction.
To calculate the total displacement, we use vector addition. Since the displacements are in different directions, we need to calculate the resultant vector.
We can use the Pythagorean theorem to find the magnitude of the resultant vector:
Resultant magnitude = sqrt((-80)^2 + (-100)^2)
≈ sqrt(6400 + 10000)
≈ sqrt(16400)
≈ 128 km
To find the direction of the resultant vector, we can use trigonometry. The angle can be calculated as:
Angle = tan^(-1)(opposite/adjacent)
Angle = tan^(-1)(100/80)
Angle ≈ 51.34 degrees
The resultant vector has a magnitude of 128 km and an angle of 51.34 degrees.
Now, we can calculate the average velocity:
Average velocity = Total displacement / Total time
Average velocity = 128 km / (2 hours + 3 hours)
Average velocity = 128 km / 5 hours
Average velocity ≈ 25.6 km/h
Therefore, the average velocity of the bus is approximately 25.6 km/h in the direction of 51.34 degrees west of south.