You are piloting a small plane, and you want to reach an airport 450 km due south in 2.0 hours. A wind is blowing from the west at 75 km/h.What heading and airspeed should you choose to reach your destination in time?
Make an angle measured from S counterclockwise to heading (somewhere SE)
the Easterly component has to be 75km/hr
The resultant is S, and the heading is 450
Then TanTheta= 75/desired resultantvelocity
TanTheta= 75/(450/2)
solve for Theta.
Your airspeed should be
SinTheta= 75/desiredairspeed
solve for desired airspeed.
To determine the heading and airspeed you should choose to reach your destination in time, you need to consider the effects of wind on your flight.
Step 1: Calculate the ground speed:
Ground speed is the speed at which the plane is moving relative to the ground. It can be calculated by subtracting the wind speed (75 km/h) from the airspeed.
Ground speed = Airspeed - Wind speed
Step 2: Calculate the distance covered in 2.0 hours:
The distance covered is given as 450 km.
Step 3: Calculate the required airspeed:
Since your destination is directly to the south, the heading should be south as well. This means there is no crosswind component to consider. Therefore, your airspeed is also equal to the ground speed.
Airspeed = Ground speed
Now, let's calculate the values:
Step 1:
Ground speed = Airspeed - Wind speed
Ground speed = Airspeed - 75 km/h
Step 2:
Distance covered = Ground speed * Time
450 km = Ground speed * 2.0 hours
Step 3:
Airspeed = Ground speed
We can now solve these equations simultaneously to find the airspeed and ground speed:
Step 1:
Airspeed - 75 km/h = Airspeed
75 km/h = 0 (subtracting Airspeed on both sides)
Step 2:
450 km = Ground speed * 2.0 hours
450 km = Airspeed * 2.0 hours (since airspeed = ground speed)
Now, solving for airspeed:
Airspeed = 450 km / 2.0 hours
Airspeed = 225 km/h
Therefore, to reach your destination in time with a wind blowing from the west at 75 km/h, you should choose a heading of due south and an airspeed of 225 km/h.