Calculating Relative Velocity: Plane and Wind Speeds | Homework Help

[Faint]

Homework Statement

An airplane is heading due south at a speed of 620 km/h. If a wind begins blowing from the southwest at a speed of 80 km/h (average), calculate the following.

(a) the velocity (magnitude and direction) of the plane relative to the ground
(566.27) km/h (5.733)° (east of south)--- I got this one

(b) how far from its intended position will it be after 10 min if the pilot takes no corrective action. [Hint: First draw a diagram.]

Homework Equations

a²+b² = c²

The Attempt at a Solution

I have gotten the answers to part A, but I am struggling on how to set up part B. I have tried doing (600/60)*10 to get 100 km/10 min, then subtracting it by the actual amount traveled. So what I have done is basically ((600/60)*10)-((566.27/60)*10)=94.378, but this is wrong.

Please help.

 

[Faint]

I solved this. It is ((80/60) * 10) = 13.3333. This is the amount the wind throws the plane off.

 

[baba89]

In order to calculate how far from its intended position the plane will be after 10 minutes, we need to first determine how far the plane travels in 10 minutes. This can be done by using the formula distance = speed x time. In this case, the speed of the plane is 620 km/h and the time is 10 minutes, so the distance traveled is (620 km/h)(10 min) = 6200 km.

Next, we need to consider the effect of the wind on the plane's movement. We know that the wind speed is 80 km/h and it is blowing from the southwest. This means that the wind is blowing in a direction that is 45 degrees south of west. In order to determine the component of the wind that is acting against the plane's movement, we can use trigonometry. The component of the wind that is acting against the plane's movement can be represented by the formula (80 km/h)sin(45).

To determine the total distance that the plane will be from its intended position after 10 minutes, we need to subtract the component of the wind acting against the plane's movement from the distance traveled by the plane. This can be represented by the formula 6200 km - (80 km/h)sin(45) x (10 min).

Using a calculator, we can determine that the total distance the plane will be from its intended position after 10 minutes is approximately 6172 km. This means that the plane will be approximately 28 km off course after 10 minutes if the pilot takes no corrective action.

It is important for pilots to take into account the effects of wind on their flight path in order to ensure that they reach their intended destination. Calculations like these are crucial for safe and efficient air travel.