Question
in a race, a boat travels a distance of 220m [E40N] and then rounds a buoy and travels a distance of 360m [N30W] to the finish line. the whole trip takes 22 seconds. determine the displacement and average velocity of the boat.
Answers
GPT 3.5
To determine the displacement of the boat, we can calculate the sum of the displacement vectors for each leg of the race.
For the first leg, the boat travels 220m towards the east while heading 40 degrees north of the east direction. To find the horizontal component, we can use the cosine function:
Horizontal component = 220m * cos(40°) ≈ 168.69m towards the east
To find the vertical component, we can use the sine function:
Vertical component = 220m * sin(40°) ≈ 141.46m towards the north
For the second leg, the boat travels 360m towards the north while heading 30 degrees west of the north direction. To find the horizontal component, we can use the cosine function:
Horizontal component = 360m * cos(60°) ≈ -180m towards the west
To find the vertical component, we can use the sine function:
Vertical component = 360m * sin(60°) ≈ 311.06m towards the north
To find the total displacement, we sum the horizontal and vertical components:
Horizontal displacement = 168.69m - 180m ≈ -11.31m
Vertical displacement = 141.46m + 311.06m ≈ 452.52m
Therefore, the displacement of the boat is ≈ -11.31m [W11.31N] + 452.52m [N].
To calculate the average velocity of the boat, we divide the total displacement by the time taken:
Average velocity = Displacement / Time
Average velocity = (-11.31m[W11.31N] + 452.52m[N]) / 22s
The direction of the average velocity is the same as the direction of the total displacement, which is [N].
For the first leg, the boat travels 220m towards the east while heading 40 degrees north of the east direction. To find the horizontal component, we can use the cosine function:
Horizontal component = 220m * cos(40°) ≈ 168.69m towards the east
To find the vertical component, we can use the sine function:
Vertical component = 220m * sin(40°) ≈ 141.46m towards the north
For the second leg, the boat travels 360m towards the north while heading 30 degrees west of the north direction. To find the horizontal component, we can use the cosine function:
Horizontal component = 360m * cos(60°) ≈ -180m towards the west
To find the vertical component, we can use the sine function:
Vertical component = 360m * sin(60°) ≈ 311.06m towards the north
To find the total displacement, we sum the horizontal and vertical components:
Horizontal displacement = 168.69m - 180m ≈ -11.31m
Vertical displacement = 141.46m + 311.06m ≈ 452.52m
Therefore, the displacement of the boat is ≈ -11.31m [W11.31N] + 452.52m [N].
To calculate the average velocity of the boat, we divide the total displacement by the time taken:
Average velocity = Displacement / Time
Average velocity = (-11.31m[W11.31N] + 452.52m[N]) / 22s
The direction of the average velocity is the same as the direction of the total displacement, which is [N].