A truck travels beneath an airplane that is moving 120 km/h at an angle of 24◦
to the ground.
How fast must the truck travel to stay beneath the airplane?
Answer in units of km/h
What is the magnitude of the vertical component of the velocity of the plane?
Answer in units of km/h
1.V = hor. = 120cos24 = 109.6km/h.
2. V = ver. = 120sin24 = 48.8km/h.
Why did the truck want to stay beneath the airplane? Because it wanted to be a "ground" supporter! 🤡
To determine how fast the truck must travel to stay beneath the airplane, we need to consider the horizontal and vertical components of the airplane's velocity.
Since the truck is staying beneath the airplane, it means it also has to match the horizontal component of the airplane's velocity. So, the truck must travel at the same speed as the airplane's horizontal component, which is 120 km/h.
Now, let's talk about the magnitude of the vertical component of the airplane's velocity.
To find this, we need to use trigonometry. We know that the angle between the airplane's velocity and the ground is 24 degrees.
The formula to calculate the vertical component of velocity is: Velocity_vertical = Velocity * sin(angle)
So, Velocity_vertical = 120 km/h * sin(24 degrees)
Calculating this, we find that the magnitude of the vertical component of the airplane's velocity is approximately 50.93 km/h.
So, to sum it up:
- The truck must travel at the same speed as the airplane's horizontal component, which is 120 km/h.
- The magnitude of the vertical component of the airplane's velocity is approximately 50.93 km/h.
Hope that puts a smile on your face, happy travels! 🚛✈️
To determine how fast the truck must travel to stay beneath the airplane, we need to analyze the components of the airplane's velocity.
Let's consider the horizontal and vertical components of the airplane's velocity.
Horizontal component: The horizontal component of the airplane's velocity is given by Vx = V * cos(angle), where V is the magnitude of the velocity (120 km/h) and the angle is 24 degrees.
Vx = 120 km/h * cos(24) ≈ 112.31 km/h
Vertical component: The magnitude of the vertical component of the airplane's velocity is given by Vy = V * sin(angle).
Vy = 120 km/h * sin(24) ≈ 49.07 km/h
To stay beneath the airplane, the truck needs to have the same horizontal component of velocity as the airplane. Therefore, the truck must travel at a speed of approximately 112.31 km/h.
The magnitude of the vertical component of the velocity of the plane is approximately 49.07 km/h.
To find the speed at which the truck must travel to stay beneath the airplane, we need to consider their relative velocities. The horizontal component of the airplane's velocity does not affect the truck since it moves in the same direction.
So, we only need to focus on the vertical component of the airplane's velocity. The vertical velocity of the airplane can be found by multiplying the total velocity by the sine of the angle with the ground.
Vertical component of velocity of airplane = total velocity × sin(angle with ground)
= 120 km/h × sin(24°)
To find the magnitude of the vertical component of the velocity of the plane, we calculate:
Magnitude of vertical component of velocity = |Vertical component of velocity|
= |120 km/h × sin(24°)|
Now, to determine how fast the truck must travel to stay beneath the airplane, it must match the magnitude of the vertical component of the airplane's velocity. Therefore, the speed of the truck must be equal to the magnitude of the vertical component of the airplane's velocity.
Speed of the truck = |Magnitude of vertical component of velocity|
= |120 km/h × sin(24°)|
Now, let's calculate the values.
Using a calculator, we find:
Vertical component of velocity of airplane ≈ 120 km/h × sin(24°) ≈ 49.167 km/h
Magnitude of vertical component of velocity ≈ |49.167 km/h| ≈ 49.167 km/h
So, the speed at which the truck must travel to stay beneath the airplane is approximately 49.167 km/h.