Using relative motion to find direction and time of a boat

• PAstudent
In summary, the motorboat must be pointed at an angle of 21.8 degrees with respect to east in order to move due north with respect to the riverbank. The time required for the motorboat to cross the 542 meter wide river is approximately 50.3 seconds. The usual convention for direction is that due east is horizontal and to the right, while due north is vertical and pointing upwards. The resultant vector must be vertical for the boat to travel due north.
PAstudent

Homework Statement

A motorboat can move with a velocity of 10.0 m/s, with respect to the water in a river. The river is flowing at 4.00 m/s due east. (a) Calculate the direction (Give the angle with respect to one of the compass directions.) the motorboat must be pointed so that it moves due north with respect to the riverbank? (b) The river is 542 meters wide; calculate the time required for this motorboat to cross the river if it is pointed in the direction calculated in part a.

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The Attempt at a Solution

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I drew this picture then I found the angle by using arctan(4/10)= 21.8 degrees. My first question is how do you know how to tell the direction it is heading in like west of north or like east of north? Then, I used Pythagorean theorem to find the diagonal vector and it was 10.77 m/s. Does this seem correct so far so that I can find the time?

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If the horizontal vector in your diagram represents the river velocity, I think you drew the diagram backwards.

The usual convention is, due east means the vector points to the right of the page and is horizontal. Due North points to the top of the page and is vertical.

You want the boat to travel due north, which suggests to me that the resultant vector must be vertical.

I just thought that the vertical vector was the velocity of the boat with respect to the water, the horizontal was velocity of water with respect to ground, and the diagonal was velocity of boat with respect to ground. That's how my teacher did it, but he isn't very clear in his directions

1. What is relative motion?

Relative motion is the movement of an object in relation to another object. It takes into account both the speed and direction of both objects to determine their relative positions.

2. How can relative motion be used to find the direction of a boat?

To find the direction of a boat using relative motion, you would need to know the speed and direction of both the boat and another fixed object, such as the shore or a buoy. By comparing the two, you can calculate the direction in which the boat is moving.

3. How can relative motion be used to find the time of a boat?

To find the time of a boat using relative motion, you would need to know the distance between the boat and another fixed object, as well as the speed of the boat. By measuring the time it takes for the boat to travel that distance, you can calculate its speed and use that information to determine the time it will take to reach a certain point.

4. What factors can affect the accuracy of using relative motion to find direction and time of a boat?

The accuracy of using relative motion to find direction and time of a boat can be affected by factors such as changes in wind or current speed, human error in measuring distances and speeds, and unexpected changes in the boat's speed or direction.

5. How can relative motion be applied in real-life situations?

Relative motion is commonly used in navigation, such as in determining the course and speed of ships and airplanes. It can also be used in sports, such as in calculating the speed and direction of a ball in motion. Additionally, relative motion is an important concept in understanding the movement of celestial bodies in astronomy.

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