Question

A scientist flying above the ocean drops buoys into the water to track ocean currents. The plane is flying at a height of 500 meters horizontally at a constant velocity while the scientist drops the buoys straight down. After the buoy is dropped the plane travels a horizontal distance of 400 meters. How far vertically does the buoy fall?

Answer 1

The buoy falls approximately 0.16 meters vertically.

Step-by-step explanation:

When the scientist drops the buoys straight down from the plane, the vertical distance they fall can be calculated using the equation for free fall. The equation for free fall is given by:

d = 0.5 * g * t^2

where d is the vertical distance, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time. In this case, the vertical distance can be calculated by substituting the time it takes for the plane to travel 400 meters horizontally (considering the plane's horizontal velocity) into the equation. Since the buoys are dropped straight down, the time it takes for them to fall vertically is the same as the time it takes for the plane to travel horizontally. Therefore, the vertical distance the buoy falls is approximately

d = 0.5 * 9.8 * (400/500)^2 = 0.16 meters.