A position vector has an x component of -2.5 m and a y component of 4.2. (a) What is the vector's magnitude and directions? b) suppose a spider took 10 minters to first walk -2.5m in the x direction and then 17 mintures 4.2 m in the y direction? Find the spider's average velocity vector.
To find the magnitude and direction of the vector, we can use the Pythagorean theorem and trigonometric functions.
(a) To find the magnitude of the vector, we need to calculate the square root of the sum of the squares of its components:
Magnitude = √((-2.5)^2 + (4.2)^2)
Magnitude = √(6.25 + 17.64)
Magnitude = √23.89
Magnitude ≈ 4.889 m
To find the direction of the vector, we can use inverse trigonometric functions. The angle (θ) can be calculated as:
θ = arctan(y component / x component)
θ = arctan(4.2 / -2.5)
θ ≈ -60.26°
Therefore, the magnitude of the vector is approximately 4.889 m, and the direction is approximately -60.26°.
(b) To find the average velocity vector, we need to divide the displacement vector by the total time taken.
Displacement vector = (-2.5)i + (4.2)j
Total time taken = 10 minutes + 17 minutes = 27 minutes
Average velocity vector = Displacement vector / Total time taken
Average velocity vector = [(-2.5 / 27)i + (4.2 / 27)j] m/minute
Therefore, the spider's average velocity vector is approximately (-0.093i + 0.156j) m/minute.