A sailboat heads north at 3 m/s for 1 hour and then tracks back to the southeast (at 45 degrees to north) at 2 m/s for 45 minutes.
a. How far has the boat sailed?
b. How far is it from its starting location?
Please do not post any more questions with the wrong School Subject.
Didn't you read the responses that bobpursley made to your last two erroneously labeled posts?
A) idk
B) ASK YOUR TEACHER MOTHA ******a
To find the distance the boat has sailed, we need to calculate the distances it traveled in each leg of the journey and then add them up.
a. Distance traveled north:
Speed = 3 m/s
Time = 1 hour = 60 minutes
Distance = Speed × Time = 3 m/s × 60 minutes = 180 meters
Distance traveled southeast (at 45 degrees to north):
Speed = 2 m/s
Time = 45 minutes
Note: Before we calculate the distance, let's convert the time to hours since the speed is given in meters per second.
45 minutes = 45/60 = 0.75 hours
Distance = Speed × Time = 2 m/s × 0.75 hours = 1.5 kilometers
Now, to find the total distance traveled, we sum up the distances from both legs:
Total distance = Distance traveled north + Distance traveled southeast
Total distance = 180 meters + 1.5 kilometers = 180 meters + 1500 meters = 1680 meters
Therefore, the boat has sailed a total distance of 1680 meters.
b. To find the distance from the boat's starting location, we need to find the displacement between its final position and starting position. Since the boat is moving both north and southeast, it forms a right-angled triangle.
Using trigonometry, we can find the displacement using Pythagoras' theorem (a^2 + b^2 = c^2), where c is the hypotenuse (the distance from the starting location).
Let's call the distance traveled north as a and the distance traveled southeast as b.
Using the values we calculated:
a = 180 meters
b = 1500 meters
Displacement (c)^2 = a^2 + b^2
Displacement (c)^2 = 180^2 + 1500^2
Displacement (c)^2 = 32400 + 2250000
Displacement (c)^2 = 2282400
Taking the square root of both sides:
Displacement c = sqrt(2282400) = 1512.8 meters
Therefore, the boat is approximately 1512.8 meters away from its starting location.