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°)
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°