Question

A pilot is flying a constant 215 km/h horizontally in a low-flying helicopter, wants to drop secret documents into his contact's open car which is traveling 155 km/h on a level highway 78.0 m below. At what angle (to the horizontal) should the car be in his sights when the packet is released?

A) 41.2 degrees
B) 24.8 degrees
C) 63.5 degrees
D) 29.1 degrees

Answer 1

The angle should be 41.2 degrees

Step-by-step explanation:

To determine the angle at which the car should be in the pilot's sights when the packet is dropped, we can use trigonometry. The horizontal distance traveled by the car during the time it takes for the packet to fall is equal to the horizontal component of the car's velocity multiplied by the time it takes for the packet to reach the car. This can be expressed as:

Distance = (Car's horizontal velocity) × (Time taken for the packet to fall)

Using the given values, we can substitute the car's horizontal velocity as 155 km/h (converted to m/s) and the time taken for the packet to fall as the time taken for the car to travel the horizontal distance. We can then solve for the angle using the equation:

Angle = arctan(Vertical distance / Horizontal distance)

After evaluating the expression, we find that the correct angle is 41.2 degrees.