In its approach to an airport runway, an airplane of mass 1.24 x 10^5 kg has a velocity of 75.5 m/s [11.1 degrees below the horizontal]. Determine the horizontal and vertical components of its momentum.
horizontal: 75.5*cos11.1
downward: 75.5sin11.1
Those are the velocity components, thence the momentum components is that velocity component x mass
Well, looks like this airplane is about to have a "runway" with momentum! Let's find out what this aircraft is up to.
To determine the horizontal and vertical components of momentum, we need to break down the velocity into its horizontal and vertical components. We're given that the velocity is 75.5 m/s [11.1 degrees below the horizontal].
First, let's calculate the horizontal component of the velocity. To do this, we'll use the formula:
horizontal velocity = velocity * cos(angle)
Plugging in the given values:
horizontal velocity = 75.5 m/s * cos(11.1 degrees)
Now, let's calculate the vertical component of the velocity. We'll use the formula:
vertical velocity = velocity * sin(angle)
Plugging in the given values:
vertical velocity = 75.5 m/s * sin(11.1 degrees)
Calculating those values, we find:
horizontal velocity = 75.5 m/s * cos(11.1 degrees) = 73.6 m/s
vertical velocity = 75.5 m/s * sin(11.1 degrees) = 14.0 m/s
So, the horizontal component of momentum is 73.6 kg*m/s, and the vertical component of momentum is 14.0 kg*m/s. Now let's hope this airplane's landing is as smooth as these calculations!
To determine the horizontal and vertical components of the airplane's momentum, we need to use trigonometry to separate the velocity vector into its horizontal and vertical components.
Given:
Mass of the airplane, m = 1.24 x 10^5 kg
Velocity of the airplane, v = 75.5 m/s
Angle below the horizontal, θ = 11.1 degrees
Step 1: Resolve the velocity vector into its horizontal and vertical components
The horizontal component of the velocity can be calculated using the cosine of the angle, while the vertical component can be calculated using the sine.
Horizontal component, Vx = v * cos(θ)
Vertical component, Vy = v * sin(θ)
Step 2: Calculate the momentum for each component
The momentum is given by the formula momentum = mass * velocity.
Horizontal momentum, Px = m * Vx
Vertical momentum, Py = m * Vy
Let's calculate these values:
Step 1:
Vx = 75.5 m/s * cos(11.1°)
Vx ≈ 73.4 m/s
Vy = 75.5 m/s * sin(11.1°)
Vy ≈ 14.0 m/s
Step 2:
Px = 1.24 x 10^5 kg * 73.4 m/s
Px ≈ 9.11 x 10^6 kg·m/s
Py = 1.24 x 10^5 kg * 14.0 m/s
Py ≈ 1.74 x 10^6 kg·m/s
Therefore, the horizontal component of the airplane's momentum is approximately 9.11 x 10^6 kg·m/s, and the vertical component is approximately 1.74 x 10^6 kg·m/s.
To determine the horizontal and vertical components of the momentum of the airplane, we need to use the given velocity and the mass of the airplane.
The horizontal component of the momentum can be calculated by multiplying the mass of the airplane by its horizontal velocity. Since the airplane is approaching the runway, the horizontal component of velocity remains unchanged.
Momentum in the horizontal direction = mass x horizontal velocity
Given:
Mass (m) = 1.24 x 10^5 kg
Horizontal velocity (Vx) = 75.5 m/s
Momentum in the horizontal direction (Px) = m * Vx
Substituting the given values:
Px = (1.24 x 10^5 kg) * (75.5 m/s)
Now analyze the vertical component of the momentum. The vertical component of velocity describes the change in vertical direction, represented by the angle below the horizontal.
The vertical component of momentum is the product of the mass and the vertical component of velocity.
Vertical component of velocity (Vy) = V*sin(θ)
where V is the magnitude of the velocity and θ is the angle below the horizontal.
Given:
Vertical velocity (Vy) = V * sin(θ)
Vy = 75.5 m/s * sin(11.1°)
Now, let's calculate the horizontal and vertical components of momentum:
Px = (1.24 x 10^5 kg) * (75.5 m/s)
Vy = 75.5 m/s * sin(11.1°)
By substituting the given values into the equations, you'll be able to calculate both the horizontal and vertical components of momentum for the airplane.