Find the sum u+v.

|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).

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

To find the sum of two vectors u and v, we can use vector addition. The magnitude of the resultant vector is given by the equation:

|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.