a truck beneath an airplane that is moving 180 km/h at an angle of 47 to the ground. How fast must the truck travelto stay beneath the airplane? Answer in units of km/h.
The velocity of the truck must be equal to the hor. component of the airplane's
velocity:
V = 180*Cos47.
To find out how fast the truck must travel to stay beneath the airplane, we need to split the velocity of the airplane into vertical and horizontal components.
The horizontal component of the airplane's velocity can be calculated using trigonometry. Given that the angle between the airplane's velocity vector and the ground is 47 degrees, we can find the horizontal component by using the formula:
horizontal velocity = airplane velocity * cos(angle)
In this case, the airplane velocity is 180 km/h and the angle is 47 degrees. Plugging these values into the formula gives us:
horizontal velocity = 180 km/h * cos(47°)
Next, we need to consider the vertical component of the airplane's velocity. This component will not affect the truck since the truck is moving horizontally.
Therefore, the truck only needs to match the horizontal component of the airplane's velocity to stay beneath it. Let's compute that:
horizontal velocity = 180 km/h * cos(47°)
horizontal velocity ≈ 180 km/h * 0.682
Approximating the value of cos(47°) to 0.682, we can calculate the horizontal velocity:
horizontal velocity ≈ 122.76 km/h
Therefore, the truck needs to travel at approximately 122.76 km/h in order to stay beneath the airplane.