Draw a diagram.
The resultant is just the hypotenuse of the triangle with u and v as legs.
The angle t with u is
tan(t) = 30/47
|u|=47, |v|=30, θ=90°
The magnitude of the resultant vector is _____.(Round to the nearest tenth).
Find the angle that the resultant makes with u. The angle is ____°.
(Round to the nearest degree).
The resultant is just the hypotenuse of the triangle with u and v as legs.
The angle t with u is
tan(t) = 30/47
|r| = √(u^2 + v^2 + 2uvcos(θ))
Here, |u| and |v| represent the magnitudes of vectors u and v respectively, and θ represents the angle between them.
In this case, |u| = 47, |v| = 30, and θ = 90°.
Substituting the values into the equation, we have:
|r| = √((47)^2 + (30)^2 + 2(47)(30)cos(90°))
|r| = √(2209 + 900 + 2820)
|r| = √(5929 + 2820)
|r| = √8749
|r| ≈ 93.5 (rounded to the nearest tenth)
Therefore, the magnitude of the resultant vector is approximately 93.5.
To find the angle that the resultant makes with u, we can use the equation:
φ = arccos((u^2 + r^2 - v^2) / (2ur))
Substituting the given values into the equation, we have:
φ = arccos((47^2 + 93.5^2 - 30^2) / (2 * 47 * 93.5))
φ = arccos((2209 + 8722.25 - 900) / (3299 * 93.5))
φ = arccos(11031.25 / 308208.5)
φ ≈ arccos(0.0358)
φ ≈ 89° (rounded to the nearest degree)
Therefore, the angle that the resultant makes with u is approximately 89 degrees.