A plane travels 4.0 km at an angle of 25◦ to the ground, then changes direction and travels 10 km at an angle of 16◦ to the ground. What is the magnitude of the plane's total displacement? Answer in units of km.

6.1 km

Explanation:

Given that a plane travels 4.0 km at an angle of 25◦ to the ground, then changes direction and travels 10 km at an angle of 16◦ to the ground. What is the magnitude of the plane's total displacement? Answer in units of km

The magnitude of the total displacement D can be calculated by using cosine formula

Ø = 25 - 16 = 9 degree

D^2 = 4^2 + 10^2 - 2 × 4 × 10 × cos 9

D^2 = 16 + 100 - 80cos9

D^2 = 116 - 79.02

D = sqrt( 36.98)

D = 6.1 m

Therefore, the magnitude of the plane's total displacement is 6.1 km