Orville walks 270 m due east. He then continues walking along a straight line, but in a different direction, and stops 230 m northeast of his starting point. How far did he walk during the second portion of the trip and in what direction?
Please I need a good explanation for this, so there looking for magnitude and direction and I just cant seem to figure it out
To find out how far Orville walked during the second portion of his trip and in what direction, we can use vector addition.
First, let's visualize the scenario. Orville starts by walking 270 m due east. This gives us a vector pointing straight to the east with a magnitude of 270 m.
Then, he continues walking along a different direction and stops 230 m northeast of his starting point. This means we have to find a vector pointing northeast with a magnitude of 230 m.
To find the magnitude and direction for the second portion of the trip, we need to determine the resultant vector of the two vectors (270 m east and 230 m northeast) using vector addition.
Step 1: Calculate the eastward component of the northeast vector.
The northeast direction is 45 degrees north of east. To find the eastward component of the northeast vector, we need to use trigonometry. The eastward component equals the magnitude (230 m) multiplied by the cosine of the angle (45 degrees). So, the eastward component is 230 * cos(45) ≈ 162.43 m.
Step 2: Calculate the northward component of the northeast vector.
To find the northward component of the northeast vector, we use the same approach as above. The northward component equals the magnitude (230 m) multiplied by the sine of the angle (45 degrees). So, the northward component is 230 * sin(45) ≈ 162.43 m.
Step 3: Combine the eastward component of the northeast vector with the east vector.
To find the total eastward component, we simply add the eastward component of the northeast vector to the east vector:
270 m + 162.43 m = 432.43 m east.
Step 4: Combine the northward component of the northeast vector with the east vector.
To find the total northward component, we add the northward component of the northeast vector to zero (since the east vector does not have any northward component):
0 m + 162.43 m = 162.43 m north.
Step 5: Find the total magnitude and direction.
To find the total magnitude, we use the Pythagorean theorem:
sqrt((432.43 m)^2 + (162.43 m)^2) ≈ 463.95 m.
For the direction, we can use the inverse tangent function:
atan(162.43 m / 432.43 m) ≈ 20.98 degrees.
Therefore, Orville walked approximately 463.95 meters during the second portion of his trip, in a direction approximately 20.98 degrees north of east.