Question

An airplane flies 20km in a direction 60 degree north of east then 30 km straight east and then 16km straight north .How far and what direction is the plane from the stating point?

Answer 1

Answer on question #84622, Physics / Mechanics | Relativity

An airplane flies $20\mathrm{km}$ in a direction 60 degree north of east then $30\mathrm{km}$ straight east and then $16\mathrm{km}$ straight north. How far and what direction is the plane from the stating point?

Solution

$$\frac {x}{2 0} = \cos 6 0 {}^ {\circ} x = 2 0 \cdot 0. 5 = 1 0$$ $$\frac {y}{2 0} = \sin 6 0 {}^ {\circ} n y = \frac {\sqrt {3}}{2} \cdot 2 0 = 1 7. 3 2$$ $$z = \sqrt {(x + 3 0) ^ {2} + (1 6 + y) ^ {2}} = 5 2. 0 6$$ $$\cos \alpha = \frac {x + 3 0}{z} = \frac {4 0}{5 2 . 0 6} = 0. 7 6 8$$ $$\alpha = 3 9. 8 {}^ {\circ}$$

Answer: $z = 52.06$ ; $\alpha = 39.8{}^{\circ}$

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