An aircraft flies at 720 km/h in a direction 40° south of west. A strong wind is blowing at 85 km/h in a direction 35° east of south. Calculate: 7.1 What distance would the aircraft have covered after 5 hours of flight?
To calculate the distance the aircraft would have covered after 5 hours of flight, we first need to find the component of the aircraft's velocity in the westward direction and the component of the wind's velocity in the southward direction.
1. Calculate the westward component of the aircraft's velocity:
cos(40°) = Adjacent/Hypotenuse
cos(40°) = w/720 km/h
w = 720 km/h * cos(40°)
w ≈ 552.72 km/h
2. Calculate the southward component of the wind's velocity:
sin(35°) = Opposite/Hypotenuse
sin(35°) = s/85 km/h
s = 85 km/h * sin(35°)
s ≈ 48.93 km/h
3. Calculate the total westward velocity of the aircraft including the wind:
Total westward velocity = Aircraft's westward velocity - Wind's southward velocity
Total westward velocity = 552.72 km/h - 48.93 km/h
Total westward velocity ≈ 503.79 km/h
4. Calculate the total distance covered after 5 hours:
Distance = Total westward velocity * time
Distance = 503.79 km/h * 5 hours
Distance = 2518.95 km
Therefore, the aircraft would have covered approximately 2518.95 km after 5 hours of flight.