To calculate the boat's resultant velocity with respect to due north, we need to use vector addition and Pythagoras' theorem.

Step 1: Identify the vectors
The boat's velocity is 17.3 m/s, N and the river's velocity is 7.33 m/s, W.

Step 2: Break down the vectors into components
The boat's velocity has only a northward component, so its components are (0, 17.3). The river's velocity has only a westward component, so its components are (-7.33, 0).

Step 3: Add the vectors
Add the corresponding components of the vectors to get the resultant vector: (0-7.33, 17.3+0) = (-7.33, 17.3).

Step 4: Calculate the magnitude of the resultant vector
Use Pythagoras' theorem to calculate the magnitude of the resultant vector: sqrt((-7.33)^2 + 17.3^2) = 18.6 m/s.

Step 5: Calculate the direction of the resultant vector
Use the arctan function to calculate the direction of the resultant vector: arctan(17.3/-7.33) = -67.3 degrees. Since we're measuring the angle with respect to due north (which we can consider as the positive y-axis), we need to add 90 degrees to this angle to get the direction from due north: -67.3 + 90 = 22.7 degrees west of north.

So, the boat's resultant velocity with respect to due north is 18.6 m/s, 22.7 degrees west of north.

Question

To calculate the boat's resultant velocity with respect to due north, we need to use vector addition and Pythagoras' theorem.

Step 1: Identify the vectors
The boat's velocity is 17.3 m/s, N and the river's velocity is 7.33 m/s, W.

Step 2: Break down the vectors into components
The boat's velocity has only a northward component, so its components are (0, 17.3). The river's velocity has only a westward component, so its components are (-7.33, 0).

Step 3: Add the vectors
Add the corresponding components of the vectors to get the resultant vector: (0-7.33, 17.3+0) = (-7.33, 17.3).

Step 4: Calculate the magnitude of the resultant vector
Use Pythagoras' theorem to calculate the magnitude of the resultant vector: sqrt((-7.33)^2 + 17.3^2) = 18.6 m/s.

Step 5: Calculate the direction of the resultant vector
Use the arctan function to calculate the direction of the resultant vector: arctan(17.3/-7.33) = -67.3 degrees. Since we're measuring the angle with respect to due north (which we can consider as the positive y-axis), we need to add 90 degrees to this angle to get the direction from due north: -67.3 + 90 = 22.7 degrees west of north.

So, the boat's resultant velocity with respect to due north is 18.6 m/s, 22.7 degrees west of north.

Knowee AI · Accepted Answer

To calculate the boat's resultant velocity with respect to due north, we need to use vector addition and Pythagoras' theorem.

Step 1: Identify the vectors
The boat's velocity is 17.3 m/s, N and the river's velocity is 7.33 m/s, W.

Step 2: Break down the vectors into components
The boat's velocity has only a northward component, so its components are (0, 17.3). The river's velocity has only a westward component, so its components are (-7.33, 0).

Step 3: Add the vectors
Add the corresponding components of the vectors to get the resultant vector: (0-7.33, 17.3+0) = (-7.33, 17.3).

Step 4: Calculate the magnitude of the resultant vector
Use Pythagoras' theorem to calculate the magnitude of the resultant vector: sqrt((-7.33)^2 + 17.3^2) = 18.6 m/s.

Step 5: Calculate the direction of the resultant vector
Use the arctan function to calculate the direction of the resultant vector: arctan(17.3/-7.33) = -67.3 degrees. Since we're measuring the angle with respect to due north (which we can consider as the positive y-axis), we need to add 90 degrees to this angle to get the direction from due north: -67.3 + 90 = 22.7 degrees west of north.

So, the boat's resultant velocity with respect to due north is 18.6 m/s, 22.7 degrees west of north.

A boat moves with a velocity of 17.3 m/s, N in a river which flows with a velocity of 7.33 m/s, west. Calculate the boat's resultant velocity with respect to due north.

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