A fisher sets out to check his fishing nets and heads 15 km/h [N] for 0.20 h. After stopping for 0.50h, he travels at 12 km/h [E] for 0.10 h to get to the next set of fishing nets.
a) What is the fisher's displacement to get to the first set of nets?
( I got 3 km [N])
b) What is the fisher's resultant displacement from the dock to the second set of nets?
(I got 3.3 km [20 degrees E of N]
c) What is the average velocity from the dock to the second set of nets?
( I got4.1 km/h [20 degrees E of N]
d) What is the average speed from the dock to the second set of nets?
(I got 5.3 km/h)
e) The fisher returns to the dock. Now what are his resultant displacement and average velocity?
(I'm not sure about this one)
Are the above answers right?
To check if the given answers are correct, let's go through each question step-by-step:
a) To find the fisher's displacement to get to the first set of nets, we need to calculate the total distance traveled in the north direction. The fisher travels at a speed of 15 km/h for 0.20 hours. The displacement can be found using the formula:
Displacement = Speed × Time
Displacement = 15 km/h × 0.20 h = 3 km [N]
Therefore, the answer to question a) is correct.
b) To find the fisher's resultant displacement from the dock to the second set of nets, we need to calculate the northward distance and the eastward distance separately. The fisher travels at a speed of 15 km/h for 0.20 h, which covers a distance of 3 km northward. After stopping for 0.50 h, the fisher travels at a speed of 12 km/h for 0.10 h, which covers a distance of 1.2 km eastward.
Using the Pythagorean theorem, we can find the resultant displacement:
Resultant Displacement = √(Northward Distance^2 + Eastward Distance^2)
Resultant Displacement = √(3^2 + 1.2^2)
Resultant Displacement = √(9 + 1.44)
Resultant Displacement ≈ √10.44
Resultant Displacement ≈ 3.2 km
To find the direction, which is the angle east of north, we can use the inverse tangent function:
θ = arctan(Eastward Distance / Northward Distance)
θ = arctan(1.2 km / 3 km)
θ ≈ arctan(0.4)
θ ≈ 21.8 degrees
Therefore, the fisher's resultant displacement from the dock to the second set of nets is approximately 3.2 km [21.8 degrees E of N].
So, the answer to question b) is slightly different, as the computed resultant displacement is 3.2 km, not 3.3 km.
c) To find the average velocity from the dock to the second set of nets, we need to calculate the average velocity vector. Average velocity is defined as the displacement divided by the total time taken.
Average Velocity = Resultant Displacement / Total Time Taken
Average Velocity = 3.2 km / (0.20 h + 0.50 h + 0.10 h)
Average Velocity ≈ 3.2 km / 0.80 h
Average Velocity ≈ 4 km/h
To find the direction, we can simply use the same angle obtained earlier:
θ ≈ 21.8 degrees
Therefore, the average velocity from the dock to the second set of nets is approximately 4 km/h [21.8 degrees E of N].
d) To find the average speed from the dock to the second set of nets, we need to calculate the total distance traveled divided by the total time taken.
Total Distance Traveled = Northward Distance + Eastward Distance
Total Distance Traveled = 3 km + 1.2 km
Total Distance Traveled = 4.2 km
Average Speed = Total Distance Traveled / Total Time Taken
Average Speed = 4.2 km / (0.20 h + 0.50 h + 0.10 h)
Average Speed = 4.2 km / 0.80 h
Average Speed = 5.25 km/h
Therefore, the average speed from the dock to the second set of nets is approximately 5.25 km/h.
e) To determine the fisher's resultant displacement and average velocity when returning to the dock, we need to calculate the northward distance and the eastward distance separately.
By applying the same calculations as in question b), but using the distances and times in reverse order, we can find the resultant displacement and average velocity for the return journey.
The resultant displacement will be the same as the initial resultant displacement (3.2 km [21.8 degrees E of N]), but in the opposite direction.
The average velocity will also be the same as the initial average velocity (4 km/h [21.8 degrees E of N]), but in the opposite direction.
Hence, the resultant displacement is 3.2 km [21.8 degrees W of S], and the average velocity is 4 km/h [21.8 degrees W of S].
To summarize:
a) The answer is correct: 3 km [N]
b) The answer has a small discrepancy: 3.2 km [21.8 degrees E of N]
c) The answer is correct: 4 km/h [21.8 degrees E of N]
d) The answer is approximately correct: 5.25 km/h
e) The fisher's resultant displacement is 3.2 km [21.8 degrees W of S], and the average velocity is 4 km/h [21.8 degrees W of S].