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.a)find total displacement from A-B average. b)speed of the trip.c)average velocity
a. displacement = sqrt(600^2+420^2)
b. distance = 600+420 = 1020
so speed = 1020/time
c.average velocity = answer from part a / time
but velocity also has a direction since it is a vector
tan angle east of north = 420/600
thanks that was very helpful 🙏
To find the total displacement from Harbour A to Harbour B, we can use Pythagoras' theorem since the boat first travels north and then east. Let's break down the problem into steps:
Step 1: Find the displacement from Harbour A to the north point.
The boat travels 600 km due north. Since it only moves in the north direction, the eastward distance is 0 km. Therefore, the displacement from Harbour A to the north point is 600 km.
Step 2: Find the displacement from the north point to Harbour B.
The boat then turns east and travels 420 km. Since it only moves in the east direction, the northward distance is 0 km. Therefore, the displacement from the north point to Harbour B is 420 km.
Step 3: Find the total displacement from A to B.
To find the total displacement, we can combine the displacements from Steps 1 and 2 using Pythagoras' theorem:
Total displacement = √(600^2 + 420^2)
= √(360000 + 176400)
= √(536400)
≈ 731.22 km (rounded to 2 decimal places)
a) The total displacement from Harbour A to Harbour B is approximately 731.22 km.
b) To find the speed of the trip, we need to know the time taken. Given that the boat starts sailing on Monday at 10:00 at Harbour A and arrives at Harbour B on Tuesday at 12:00, that means the trip took 26 hours (24 hours from Monday 10:00 to Tuesday 10:00, plus an additional 2 hours to reach 12:00).
Speed = Total distance / Time taken
= (600 km + 420 km) / 26 hours
= 1020 km / 26 hours
≈ 39.23 km/h (rounded to 2 decimal places)
b) The speed of the trip is approximately 39.23 km/h.
c) Average velocity is the total displacement divided by the time taken:
Average velocity = Total displacement / Time taken
= 731.22 km / 26 hours
≈ 28.12 km/h (rounded to 2 decimal places)
c) The average velocity of the trip is approximately 28.12 km/h.
To find the answers to these questions, we can break down the problem into smaller steps and use basic formulas for displacement, speed, and average velocity.
a) To find the total displacement from Harbour A to Harbour B, we need to find the straight-line distance between the two harbors. Since the boat first sails 600 km due north and then 420 km due east, we can use the Pythagorean theorem to find the straight-line distance between A and B.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the 600 km northward distance represents one side of the triangle, and the 420 km eastward distance represents the other side. The straight-line distance between the two harbors represents the hypotenuse.
Using the Pythagorean theorem, we can calculate the straight-line distance:
Distance^2 = (600 km)^2 + (420 km)^2
Distance = √((600 km)^2 + (420 km)^2)
Plugging in the values and calculating:
Distance = √(360000 km^2 + 176400 km^2)
Distance = √536400 km^2
Distance ≈ 732.4 km
Therefore, the total displacement from Harbour A to Harbour B is approximately 732.4 km.
b) To find the speed of the trip, we need to divide the total distance traveled by the total time taken. We can find the total time taken by subtracting the time the boat started from the time it reached Harbour B.
The boat started on Monday at 10:00 and reached Harbour B on Tuesday at 12:00, which means it took a total of 24 hours to complete the trip.
To find the speed, we divide the total distance (732.4 km) by the total time (24 hours):
Speed = Total distance / Total time
Speed = 732.4 km / 24 hours
Speed ≈ 30.5 km/h
Therefore, the speed of the trip is approximately 30.5 km/h.
c) Average velocity is defined as the total displacement divided by the total time taken.
Average Velocity = Total displacement / Total time
Average Velocity = 732.4 km / 24 hours
Average Velocity ≈ 30.5 km/h
Therefore, the average velocity of the trip is approximately 30.5 km/h.