**A rocket fires two engines simultaneously. One produces a thrust of 480 N directly forward, while the other gives a 513 N thrust at 32.4 degree above the forward direction. Find the magnitude and direction (relative to the forward direction) of the resultant force that these engines exert on the rocket.**

Resolve the 513N thrust into two components of the right angles.

On the forward side, we have 513N cos(32.4°)

At right angles, we have 513N sin(32.4°)

So…

513N cos(32.4°) = 433.14 N

513N sin(32.4°) = 274.88 N

Next, get the total forward force of the rocket.

480 N + 433.14 N = 913.14 N

And the total force at right angles:

0 + 274.88 N = 274.88 N

Next, solve the Resultant Magnitude (F) through the Pythagorean theorem.

F² = (913.14 N)² + (274.88 N)²

F² = 909383.67

F = √909383.67

F = 953.61

Now that we have resultant magnitude, find the direction by dividing total force exerted at right angles by the total force exerted at the forward side.

tanθ = 274.88 N / 913.14 N

tanθ = 0.301027225

θ = tan⁻¹ 0.301027225

θ = 16.75°