How fast must a truck travel to stay beneath an airplane that is moving 125 km/h at an angle of 35 degrees to the ground?
horizontal speed=125*cos35deg
To determine the speed at which the truck must travel to stay beneath the airplane, we need to consider the horizontal component of the airplane's velocity.
Given:
Airplane velocity = 125 km/h
Angle to the ground = 35 degrees
To find the horizontal component of the airplane's velocity, we can use trigonometry. The horizontal component is given by the equation:
Horizontal component = Airplane velocity * cos(angle)
Horizontal component = 125 km/h * cos(35 degrees)
To ensure the units are consistent, we need to convert the velocity to m/s and the angle to radians:
Horizontal component = (125 km/h * 1000 m/km) / (3600 s/h) * cos(35 degrees)
Simplifying, we get:
Horizontal component = (125 * 1000 / 3600) * cos(35 degrees) m/s
Horizontal component ≈ 34.54 m/s
Therefore, the truck must travel at a speed of approximately 34.54 m/s to stay beneath the airplane.
To solve this problem, we need to break down the velocity of the airplane into its horizontal and vertical components.
The horizontal component of the airplane's velocity can be found by multiplying the magnitude of the velocity (125 km/h) by the cosine of the angle (35 degrees):
Horizontal velocity = 125 km/h * cos(35°)
Next, we need to determine the speed at which the truck should travel to match the horizontal component of the airplane's velocity. Since the truck wants to stay beneath the airplane, it only needs to match its horizontal speed. Therefore:
Truck's required velocity = Horizontal velocity
So, to find the required velocity of the truck, we can substitute the value we found earlier:
Truck's required velocity = 125 km/h * cos(35°)
By calculating this equation, you can determine the speed that the truck must travel to stay beneath the airplane.