JOHN WANTS TO PADDLE HIS CANOE ACROSS A RIVER THAT IS 200M WIDE, HE STARTS FROM THE EAST SIDE. THE WATER CURRENT FLOWS NORTH-SOUTH AT 0.5MS^-1. IT TAKES JOHN 252S TO CROSS THE RIVER.
1. DRAW A DIAGRAM TO GRAPHICALLY REPRESENT THE VELOCTY VECTORS OF THE WATER CANOE AND THEIR RESULTANT
2.CALCULATE THE DIRECTION JOHN HEADED HIS CNOE TO FOLLOW A COURSE DUE WEST ACROSS THE RIVER
He ends up going 200 meters west in 252 seconds.
Therefore we an figure out his west velocity component:
Vw = 200/252 m/s
Meanwhile he is carried south at .5 m/s so he will have to have a north component of
Vn = .5 m/s
So we can figure the angle north of west he has to head.
tan A = Vn/Vw
Head A degrees north of west and you go straight west :)
1. To draw a diagram representing the velocity vectors of the water current and the canoe, follow these steps:
Step 1: Draw a straight line to represent the width of the river, measuring 200 meters. Label this line as "River Width."
Step 2: Mark a point on the left side of the river and label it as "Starting Point."
Step 3: Draw an arrow pointing towards the north from the starting point. Label this arrow as "Water Current Velocity" and indicate its magnitude (0.5 m/s) using small numbers or decimals.
Step 4: From the starting point, draw an arrow pointing towards the west. Label this arrow as "Canoe Velocity" and indicate its magnitude using small numbers or decimals.
Step 5: From the starting point, draw an arrow called "Resultant Velocity" that represents the combined effect of the water current and the canoe velocity. Label its magnitude and direction using small numbers or decimals.
2. To calculate the direction John should head his canoe to follow a course due west across the river, follow these steps:
Step 1: Determine the angle between the water current velocity vector and the resultant velocity vector. You can do this by using basic trigonometry.
Step 2: Take the inverse tangent of the quotient of the magnitude of the two vectors (in this case, 0.5 m/s for the water current velocity and the magnitude of the resultant velocity vector). The result will be the angle between the two vectors.
Step 3: Subtract this angle from 90 degrees (or 270 degrees if you prefer measuring angles counterclockwise). This will give you the angle at which John should head his canoe to follow a course due west across the river.
Note: It is important to convert the angle from radians to degrees if necessary.
By following these steps, you should be able to draw the diagram and calculate the direction John headed his canoe to follow a course due west across the river.