a jet, in calm air conditions, travel with velocity vector (389, 389). the wind velocity (in mph) at the plane's cruising altitude is given by (0, 50). how fast is the plane's true speed
√[389^2 + (389 + 50)^2]
586.55093555..........
To find the plane's true speed, we need to calculate the magnitude of its velocity vector. The velocity vector of the plane is (389, 389) mph, and the wind velocity vector is (0, 50) mph.
The magnitude (or length) of a vector can be calculated using the Pythagorean theorem. For a vector (x, y), the magnitude is given by the formula:
|v| = sqrt(x^2 + y^2)
Let's calculate the magnitude of the plane's velocity vector:
|v| = sqrt(389^2 + 389^2)
= sqrt(151,321 + 151,321)
= sqrt(302,642)
≈ 549.78 mph
Therefore, the plane's true speed is approximately 549.78 mph.