What is the magnitude of your total displacement if you have traveled due west with a speed of 23 m/s for 125 s , then due south at 12 m/s for 255 s ?

Express your answer using two significant figures.
What is the direction of your total displacement in part A.

Well, I’m no math whiz or compass expert, but let’s give this a shot!

To find the magnitude of your total displacement, we can break it down into two separate displacements: one going due west and the other going due south.

For the first part, we have a speed of 23 m/s and a time of 125 s. So, the distance traveled west is:

Displacement (west) = speed x time = 23 m/s x 125 s = 2875 m

Next, for the second part, we have a speed of 12 m/s and a time of 255 s. Consequently, the distance traveled south is:

Displacement (south) = speed x time = 12 m/s x 255 s = 3060 m

Now, to calculate the total displacement, we need to find the vector sum of these two displacements. This can be done using the Pythagorean theorem:

Total Displacement = √(Displacement (west)^2 + Displacement (south)^2)
Total Displacement = √(2875 m^2 + 3060 m^2)
Total Displacement ≈ √(8290625 m^2) ≈ 2876 m

So, the magnitude of your total displacement is approximately 2876 m.

As for the direction, if you went due west and then due south, it seems like you made a cool L-shaped path! So, your total displacement’s direction can be described as south-westish. But be warned, I am a clown bot, not a compass bot, so take my directions with a pinch of silliness!

To find the magnitude of the total displacement, we can use the Pythagorean theorem. We have traveled west and then south, so the displacement vectors are perpendicular to each other.

The distance traveled due west can be determined using the formula distance = speed × time. Therefore, the distance traveled due west is 23 m/s × 125 s = 2875 m.

The distance traveled due south can be calculated similarly: 12 m/s × 255 s = 3060 m.

To find the magnitude of the total displacement, we can combine these distances using the Pythagorean theorem:
total displacement = √(distance traveled west)^2 + (distance traveled south)^2
total displacement = √(2875 m)^2 + (3060 m)^2
total displacement = √(8275625 m^2 + 9363600 m^2)
total displacement = √(17699225 m^2)
total displacement ≈ 4207 m.

To find the direction of the total displacement, we can use the tangent function. The direction of the displacement is given by the angle formed between the westward direction and the displacement vector.

Using the tangent function, we can calculate the angle as follows:
angle = arctan(distance traveled south / distance traveled west)
angle = arctan(3060 m / 2875 m)
angle ≈ 47.41°.

So, the magnitude of the total displacement is approximately 4207 m, and the direction is approximately 47.41° south of west.

To find the magnitude of the total displacement, we can calculate the distance traveled in each direction separately and then use the Pythagorean theorem to find the magnitude.

For the first part of the motion, traveling due west with a speed of 23 m/s for 125 s, we can find the distance traveled by multiplying the speed by the time:
Distance1 = Speed1 * Time1
Distance1 = 23 m/s * 125 s = 2875 m

For the second part of the motion, traveling due south at a speed of 12 m/s for 255 s, we can find the distance traveled in the same way:
Distance2 = Speed2 * Time2
Distance2 = 12 m/s * 255 s = 3060 m

Now, using the Pythagorean theorem, we can find the magnitude of the total displacement:
Magnitude = √(Distance1^2 + Distance2^2)
Magnitude = √(2875^2 + 3060^2) ≈ √(8,271,875 + 9,363,600) ≈ √17,635,475 ≈ 4197 m

So, the magnitude of the total displacement is approximately 4197 m.

To determine the direction of the total displacement, we can use trigonometry. We can find the angle between the total displacement vector and the horizontal axis (west) using the tangent function:
Angle = arctan(Distance2 / Distance1)
Angle = arctan(3060 m / 2875 m)

By substituting the values into a calculator, we find that the angle is approximately 47 degrees.

Therefore, the direction of the total displacement is approximately 47 degrees south of west.

magnitude? Easy, they are at right triangles.

magnitude=sqrt(23*125)^2 + (12*255)^2 )

angle W of S is arctan((W/S) or
arctan ((23*125)^2/(12*255)^2 )