A plane travels 2.5 KM at an angle of 35 degrees to the ground, then changes direction and travels 5.2 km at an angle of 22 degrees to the ground. What is the magnitude and direction of the planes total displacement?

We can solve for the resultant x and y components by using the sine and cosine functions.

resultant x = 2.5 cos 35 + 5.2 cos 22 = 6.87 km

resultant y = 2.5 sin 35 + 5.2 sin 22 = 3.38 km

The resultant displacement is calculated using hypotenuse equation:

displacement = sqrt (6.87^2 + 3.38^2)

displacement = 7.66 km

The resultant angle is:

θ = tan^-1 (3.38 / 6.87)

θ = 26.20°

Therefore the magnitude and direction is:

7.66 km, 26.20° to the ground