Find the vector sum of a 65 m/s wind acting due east and a 32 m/s wind due west. Give the magnitude and direction please.
To find the vector sum of the winds, we can first assign positive and negative signs to the velocities, depending on their directions. Let's take eastwards as positive and westwards as negative:
- The 65 m/s wind acting due east will be represented as +65 m/s.
- The 32 m/s wind acting due west will be represented as -32 m/s.
To get the vector sum, we need to add these two vectors together by combining their magnitudes and taking into account their directions. Adding a positive and a negative value is the same as subtracting them, so we'll subtract the magnitude of the westward wind from the magnitude of the eastward wind:
65 m/s - 32 m/s = 33 m/s
The magnitude of the resultant vector (or the vector sum) is 33 m/s.
Now, let's determine the direction of the resultant vector. Since we assigned eastwards as positive and westwards as negative, the resultant vector will be pointing towards the east, as the magnitude of the eastward wind is greater than the magnitude of the westward wind.
Therefore, the vector sum of the two winds is 33 m/s, acting due east.