A sailboat runs before the wind with a constant speed of 4.0m/s in a direction 34∘ north of west. how far west has the sail boat traveled in 29 minutes
distance= speedwest*time
= 4ms/*cos34*29min*60sec/min
To find out how far west the sailboat has traveled, we can first calculate its displacement in westward direction using the given information.
1. Start by converting the time from minutes to seconds since the speed is given in meters per second. We know that 1 minute is equal to 60 seconds. So, 29 minutes is equal to 29 × 60 = 1740 seconds.
2. Next, we need to find the component of the sailboat's velocity in the westward direction. Since it is running "north of west," we need to consider the angle between the westward direction and the direction the boat is moving. The angle is given as 34∘ north of west.
3. To calculate the westward component of the velocity, we use the formula:
westward velocity = total velocity × cosine(angle)
westward velocity = 4.0 m/s × cos(34∘)
Using a calculator, we can find that cos(34∘) ≈ 0.829, so:
westward velocity ≈ 4.0 m/s × 0.829 ≈ 3.316 m/s
4. Now that we know the westward velocity, we can calculate the displacement in the westward direction using the formula:
displacement = velocity × time
displacement = 3.316 m/s × 1740 s
Using a calculator, we find that the displacement in the westward direction is approximately 5762.64 meters.
Therefore, the sailboat has traveled approximately 5762.64 meters west in 29 minutes.