A plane directly east at a velocity of 860 km/h for 45 min and then travels directly west with a velocity of 720 km/h for 1h and 30 min. Find the following values for this plane, expressed in km and km/h:
a) Total displacement
b) Total distance
c) Average velocity
d) Average speed
displacement: 860*.75-720*1.5 East
distance : add the above
avgvelocity=displacement/total time
avg speed: distance/total time
To solve this question, we will use the formulas:
Displacement = Final position - Initial position
Distance = Total path traveled
Average Velocity = Total displacement / Total time
Average Speed = Total distance / Total time
Let's calculate the values step by step.
a) Total Displacement:
The plane is moving in opposite directions, so we need to calculate the displacement for each segment separately and then find the sum.
For the first segment:
Velocity = 860 km/h
Time = 45 min = 45/60 = 0.75 hours
Displacement1 = Velocity * Time = 860 km/h * 0.75 hours = 645 km
For the second segment:
Velocity = 720 km/h
Time = 1.5 hours
Displacement2 = Velocity * Time = 720 km/h * 1.5 hours = 1080 km
Total Displacement = Displacement1 - Displacement2 = 645 km - 1080 km = -435 km
Therefore, the total displacement is -435 km (west direction).
b) Total Distance:
To find the total distance, we need to add the distances traveled during each segment.
Distance1 = Velocity * Time = 860 km/h * 0.75 hours = 645 km
Distance2 = Velocity * Time = 720 km/h * 1.5 hours = 1080 km
Total Distance = Distance1 + Distance2 = 645 km + 1080 km = 1725 km
Therefore, the total distance traveled by the plane is 1725 km.
c) Average Velocity:
Average velocity is the total displacement divided by the total time.
Total Time = Time1 + Time2 = 0.75 hours + 1.5 hours = 2.25 hours
Average Velocity = Total Displacement / Total Time = -435 km / 2.25 hours
Therefore, the average velocity of the plane is approximately -193 km/h (west direction).
d) Average Speed:
Average speed is the total distance divided by the total time.
Average Speed = Total Distance / Total Time = 1725 km / 2.25 hours
Therefore, the average speed of the plane is approximately 767 km/h.