A vector has components Ax = 44 m and Ay = 30 m. Find the length of the vector vector A and the angle it makes with the x axis.
in meters and in degrees
|A| = sqrt (44^2+30^2)
angle = tan^-1 (30/44)
To find the length of a vector with given components Ax and Ay, you can use the Pythagorean theorem. The length (magnitude) of a vector A is given by:
|A| = √(Ax^2 + Ay^2)
Using the given components, we can calculate the magnitude of vector A as follows:
|A| = √(44^2 + 30^2)
|A| = √(1936 + 900)
|A| = √2836
|A| ≈ 53.23 m
Therefore, the length of vector A is approximately 53.23 m.
To find the angle that a vector makes with the x-axis, you can use the formula:
θ = arctan(Ay / Ax)
Plugging in the given values, we can calculate the angle (θ):
θ = arctan(30 / 44)
θ ≈ 35.88°
Therefore, the angle that vector A makes with the x-axis is approximately 35.88 degrees.