Question

a) Aircraft ‘A’ travels at a velocity of 300 km/h in a direction 600 South of East. The wind direction is due North with a velocity of 70 km/h. Determine the resultant velocity of the aircraft.

b) Aircraft ‘B’ is sighted from A and travels at a velocity of 200 km/h in a direction 300 east of north and crosses this path at a point 2.5 Km ahead. Find the relative velocity of B with respect to A and what will be their closest distance of approach.

c) Draw the space diagram and velocity vector diagram for both the cases.

Answer 1

Answer on question #80022, Physics / Mechanics

a) Aircraft 'A' travels at a velocity of $300\mathrm{km/h}$ in a direction 600 South of East. The wind direction is due North with a velocity of $70\mathrm{km/h}$. Determine the resultant velocity of the aircraft.

b) Aircraft 'B' is sighted from A and travels at a velocity of $200\mathrm{km/h}$ in a direction 300 east of north and crosses this path at a point 2.5 Km ahead. Find the relative velocity of B with respect to A and what will be their closest distance of approach.

c) Draw the space diagram and velocity vector diagram for both the cases.

Solution

a) The resultant velocity of the aircraft:

$$v_{res A} = v_{Aircraft A} - v_{wind} = 300 - \cos(4\hat{\xi}) = 275.25 \ \frac{\mathrm{km}}{\mathrm{h}}$$

b) $v_{res B} = v_{Aircraft B} + v_{wind} = 200 + \cos(4\hat{\xi}) = 224.25 \ \frac{\mathrm{km}}{\mathrm{h}}$

relative velocity of B with respect to A

$$v_{relative} = \sqrt{v_{res A}^2 + v_{res B}^2} = 368.66 \ \frac{\mathrm{km}}{\mathrm{h}}$$

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