a train moving at a constant speed of 100km/h travels east for 40 minutes..then 30 degree east of north for 20 minutes...and finally west for 30 minutes..what's the trains average velocity for the trip at which direction?
Add the vector displacements and divide the result by total elapsed time.
To calculate the average velocity, we need to consider both the magnitude (speed) and direction of the train's displacement.
Let's break down the given information step by step:
1. The train travels east for 40 minutes at a constant speed of 100 km/h. Since the train is moving only in the east direction, the displacement in this leg is purely in the east direction.
2. Then, the train changes its direction and moves 30 degrees east of north for 20 minutes. To determine the displacement in this leg, we need to convert the 30-degree angle east of north into a component in the north and east directions.
- The north component can be calculated as: north_component = (100 km/h) * sin(30 degrees)
- The east component can be calculated as: east_component = (100 km/h) * cos(30 degrees)
3. Finally, the train travels west for 30 minutes. Since the train is moving only in the west direction, the displacement in this leg is purely in the west direction.
To calculate the average velocity, we need to consider the total displacement and total time taken for the entire trip.
1. Total displacement:
- Displacement in the east direction: 100 km/h * (40 minutes / 60 minutes) = 66.7 km (rounded to one decimal place)
- Displacement in the north direction (from step 2): north_component * (20 minutes / 60 minutes) = north_component * 0.33 (since 20 minutes is 1/3 of an hour)
- Displacement in the east direction (from step 2): east_component * (20 minutes / 60 minutes) = east_component * 0.33 (since 20 minutes is 1/3 of an hour)
- Displacement in the west direction: 100 km/h * (30 minutes / 60 minutes) = 50 km
The total displacement can be calculated by adding the individual displacements:
total_displacement = 66.7 km + north_component * 0.33 + east_component * 0.33 - 50 km
2. Total time:
The total time taken for the entire trip is the sum of the times taken in each leg:
total_time = 40 minutes + 20 minutes + 30 minutes = 90 minutes
Now, we can calculate the average velocity of the train:
average_velocity = total_displacement / total_time
The direction of the average velocity can be determined by considering the resulting displacement. If the total displacement is in the east direction, the average velocity will be in the east direction. If the total displacement is in the west direction, the average velocity will be in the west direction. If the total displacement has both north and east components, it means the train moved in a diagonal direction.
Please note that more specific information about the east-of-north angle and the specific values of north_component and east_component would be required to provide a precise numerical answer.