What is the airspeed relative to the ground of an airplane with an airspeed of 120km/h when it is in a 90-km/h crosswind?
You should draw a vector diagram for this. Using a scale of say 1cm=10km/hr.
Draw a straight line up the page 12cm to represent northwards at 120km/hr.
Where this line finishes, draw a line from left to right 9cm long to represent a crosswind of 90km/hr.
Once you've done that, draw a line from the very start point to the end point, giving you a triangle.
Measure it's length, it will be 15 cm long, meaning that the airplane is actually flying in a north-easterly direction at 150km/hr. the line you've drawn actually shows you the path the aircraft would fly in those conditions.
You could also use math to work out the speed (remember you've just drawn a right angled triangle)
The hypotenuse will be the speed of the aircraft.
x^2 = 120^2+90^2
x^2 = 22500
x = 150
To determine the airspeed relative to the ground of an airplane with an airspeed of 120 km/h in a 90 km/h crosswind, we can use vector addition.
Step 1: Draw a diagram
Draw a diagram to represent the situation. Let's use a scale where 1 cm represents 10 km/h.
Step 2: Represent the airspeed and crosswind vectors
Draw a vector to represent the airspeed of 120 km/h. Label it as "Airspeed" or "A". It should be pointing in the direction the plane is flying.
Next, draw another vector to represent the crosswind of 90 km/h. Label it as "Crosswind" or "C". It should be perpendicular to the airspeed vector.
Step 3: Find the resultant vector
To find the resultant vector, add the two vectors together. Draw a vector starting from the tail of the airspeed vector to the head of the crosswind vector. This vector represents the resultant of the airspeed and crosswind vectors.
Step 4: Measure the resultant vector
Using a ruler, measure the length of the resultant vector on your diagram. Each cm on your diagram represents 10 km/h. Convert this measurement to km/h by multiplying by the scale factor. The measured length of the resultant vector represents the airspeed relative to the ground.
Step 5: Calculate the final answer
Multiply the measured length of the resultant vector by the scale factor to get the airspeed relative to the ground.
For example, if the measured length of the resultant vector is 5 cm, the airspeed relative to the ground would be 5 cm multiplied by 10 km/h/cm, which equals 50 km/h.
Therefore, the airspeed relative to the ground of the airplane with an airspeed of 120 km/h in a 90 km/h crosswind is 50 km/h.
To find the airspeed relative to the ground of an airplane with a given airspeed and a crosswind, you can use vector addition.
Step 1: Break down the airspeed and crosswind velocities into their respective components. The airspeed is given as 120 km/h, and the crosswind is given as 90 km/h. Since the crosswind is perpendicular to the direction of the airplane, it only affects the airplane's groundspeed, not its airspeed. Let's call the airspeed component in the direction of the airplane's travel "Vx" and the crosswind component "Vy."
Step 2: Determine the magnitude and direction of the resultant vector. The magnitude of the resultant vector is found by using the Pythagorean theorem: magnitude = √(Vx^2 + Vy^2). The direction of the resultant vector can be determined by using trigonometry. We can find the angle "θ" using the equation: θ = arctan(Vy/Vx).
Step 3: Calculate the airspeed relative to the ground. Since the crosswind only affects the groundspeed, the airspeed relative to the ground can be found by subtracting the crosswind component from the magnitude of the resultant vector: airspeed relative to the ground = magnitude - Vy.
Let's calculate it step by step:
Step 1: The airspeed component in the direction of the airplane's travel, Vx, is 120 km/h (given). The crosswind component, Vy, is 90 km/h (given).
Step 2: Calculate the magnitude and direction of the resultant vector:
Magnitude = √(Vx^2 + Vy^2) = √(120^2 + 90^2) = √(14400 + 8100) = √(22500) = 150 km/h (approx.)
Direction (θ) = arctan(Vy/Vx) = arctan(90/120) = arctan(0.75) ≈ 36.87 degrees.
Step 3: Calculate the airspeed relative to the ground:
Airspeed relative to the ground = magnitude - Vy = 150 - 90 = 60 km/h.
Therefore, the airspeed relative to the ground of the airplane is 60 km/h when it has an airspeed of 120 km/h and is in a 90 km/h crosswind.