How fast must a truck travel to stay beneath an airplane that is moving 139km/hr at an angle of 25° to the ground?
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To solve this problem, we need to understand the motion of the airplane and the relative motion of the truck with respect to the airplane.
First, let's analyze the motion of the airplane:
The airplane is moving at a speed of 139 km/hr at an angle of 25° to the ground. This can be represented by two components: the horizontal component and the vertical component of the velocity.
The horizontal component of the velocity can be calculated using trigonometry:
Horizontal Velocity = Velocity × cos(angle)
Horizontal Velocity = 139 km/hr × cos(25°)
The vertical component of the velocity can also be calculated using trigonometry:
Vertical Velocity = Velocity × sin(angle)
Vertical Velocity = 139 km/hr × sin(25°)
Next, let's consider the motion of the truck:
To stay beneath the airplane, the truck must have the same horizontal component of velocity as the airplane. Therefore, the speed of the truck must be equal to the horizontal velocity of the airplane.
So, to answer your question, the truck must travel at a speed equal to the horizontal component of the airplane's velocity. Let's calculate it:
Horizontal Velocity = 139 km/hr × cos(25°)
Horizontal Velocity ≈ 139 km/hr × 0.9063
Horizontal Velocity ≈ 126.3 km/hr
Therefore, the truck must travel at a speed of approximately 126.3 km/hr to stay beneath the airplane.