a boeing 747 can travel up to 254m/s. The pilot must travel from vancouver to calgary, which is located 3.0x10^2km [N] and 7.0x10^2km [E]. there is strong wind blowing at 50.0m/s [SE].
To determine the time it takes for the pilot to travel from Vancouver to Calgary, we need to consider the plane's speed, the distance to be traveled, and the effect of the wind. We can break down the problem into horizontal and vertical components.
Horizontal Component:
The horizontal component involves the distance traveled in an eastward direction. Given that the distance is 7.0x10^2km [E], we can convert it to meters by multiplying by 1000.
Distance = 7.0x10^2km = 7.0x10^5m [E]
To account for the wind blowing at 50.0m/s [SE], we need to find the resultant velocity. Since we have the velocity of the plane (254m/s) and the wind speed (50.0m/s), we can use vector addition:
Resultant velocity = √(plane velocity^2 + wind velocity^2)
Resultant velocity = √((254m/s)^2 + (50.0m/s)^2)
Now, we have the resultant velocity, which is the speed of the plane relative to the ground, considering the wind. We can use this velocity to determine the time it takes to travel the horizontal distance.
Time = Distance / Resultant velocity
= 7.0x10^5m [E] / Resultant velocity
Vertical Component:
The vertical component involves the distance traveled in a northward direction. Given that the distance is 3.0x10^2km [N], we can convert it to meters by multiplying by 1000.
Distance = 3.0x10^2km = 3.0x10^5m [N]
Since there is no wind in the vertical direction, the vertical component is not affected by wind speed.
Now, we have the vertical distance traveled, and we can use this distance to determine the time it takes.
Time = Distance / plane velocity
= 3.0x10^5m [N] / 254m/s
Finally, we add the time taken for the horizontal component and the vertical component to get the total travel time.
Total travel time = Time (horizontal) + Time (vertical)
By calculating these values, we can determine the time it takes for the pilot to travel from Vancouver to Calgary, considering the wind conditions.