An airplane travels at 144 km/h toward the
northeast.
What is the northern component of its ve-
locity?
Answer in units of km/h.
North component= 144km/hr * Cos45
To find the northern component of the velocity, we can use trigonometry.
The airplane is traveling toward the northeast, which is a 45-degree angle relative to the north axis.
We can use the formula:
North component of velocity = Total velocity * cosine (angle)
Given that the total velocity is 144 km/h and the angle is 45 degrees, we can calculate it as follows:
North component of velocity = 144 km/h * cos(45°)
Using the calculator, the cosine of 45 degrees is approximately 0.707.
North component of velocity = 144 km/h * 0.707
Calculating this gives:
North component of velocity ≈ 101.808 km/h
So, the northern component of its velocity is approximately 101.808 km/h.
To find the northern component of the airplane's velocity, we need to break down its motion into its northward and eastward components. Since the airplane is traveling toward the northeast, we can use the concept of vectors and trigonometry to solve this problem.
Step 1: Draw a diagram:
Draw a diagram of the airplane's motion, with the northeast direction as a 45-degree angle relative to the north and east directions. This will help you visualize the problem better.
Step 2: Define the components:
Let's define the northward component of the velocity as Vn and the eastward component of the velocity as Ve.
Step 3: Use trigonometry:
Since the angle between the northeast direction and the north direction is 45 degrees, we can use trigonometric functions to relate the components of the velocity.
In this case, we can use the sine function to find the northward component:
sin(45) = Vn / 144
Step 4: Solve for Vn:
Rearrange the equation to solve for Vn:
Vn = 144 * sin(45)
Step 5: Calculate Vn:
We can use a scientific calculator or an online calculator to find the value of sin(45):
sin(45) ≈ 0.7071
Now, substitute the value of sin(45) into the equation to calculate Vn:
Vn = 144 * 0.7071 ≈ 101.7964 km/h
So, the northern component of the airplane's velocity is approximately 101.8 km/h.