A boat start sailing on Monday 10:00 at harbour A and sails 600km due north. Later it turns east for a further 420km to reach harbour B on Tuesday at 12:00..calculate the average velocity of the trip
total distance: 600+420=1020 km
total time: 1 day + 2hr = 26 hr
avg speed: 1020km/26hr = 39.23 km/hr
total displacement = √(600^2+420^2) = 732.39 km
in a direction θ where tanθ = 420/600, so θ = 35°
So, avg velocity is 732.39/26 = 28.17 km/hr at N35°E
To calculate the average velocity of the trip, we need to determine the total distance traveled and the total time taken.
The boat traveled 600 km due north and then turned east and traveled an additional 420 km. So, the total distance traveled is 600 km + 420 km = 1020 km.
The boat started sailing on Monday at 10:00 and arrived at the destination on Tuesday at 12:00. The total time taken is 26 hours.
Now, we can calculate the average velocity using the formula:
Average velocity = Total distance / Total time
Average velocity = 1020 km / 26 hours
Therefore, the average velocity of the trip is approximately 39.23 km/h.
To calculate the average velocity of the trip, we need to divide the total displacement of the boat by the total time taken.
First, let's calculate the displacement of the boat. The boat traveled 600 km due north and later turned east for 420 km. These two components can be represented as a right-angled triangle, where the hypotenuse represents the direct displacement from harbor A to harbor B.
Using the Pythagorean theorem, we can find the hypotenuse:
Distance = sqrt(600^2 + 420^2)
Distance = sqrt(360,000 + 176,400)
Distance = sqrt(536,400)
Distance ≈ 732.65 km
So, the displacement of the boat is approximately 732.65 km.
Next, let's calculate the time taken for the trip. The boat started sailing on Monday at 10:00 and reached harbor B on Tuesday at 12:00. This means the trip lasted for 26 hours (Monday 10:00 to Tuesday 12:00).
Now, we can calculate the average velocity:
Average Velocity = Displacement / Time Taken
Average Velocity = 732.65 km / 26 hours
Average Velocity ≈ 28.18 km/h
Therefore, the average velocity of the trip is approximately 28.18 km/h.