The movie "The Gods Must Be Crazy" begins with a pilot dropping a bottle out of an airplane. A surprised native below, who thinks it is a message from the gods, recovers it. If the plane from which the bottle was dropped was flying at a height of 500 m, and the bottle lands 400 m horizontally from the initial dropping point, how fast was the plane flying when the bottle was released? Draw a 2-dimensional motion map for the velocities and another for the acceleration.

1) The Speed of the plane is approximately 39.596 m/s

2) Please find attached the required velocity and acceleration graphs

Explanation:

1) The height at which the plane was flying, h = 500 m

The location the bottle lands from the initial dropping point = 400 m

The time it takes the bottle to land is given by the equation for free fall as follows;

h = 1/2·g·t²

Where;

g = The acceleration due to gravity = 9.8 m/s²

t = √(h/(1/2·g) = √(500/(1/2×9.8) ≈ 10.102

The Speed of the plane = The horizontal velocity of the bottle = 400/10.102 ≈ 39.596

The Speed of the plane ≈ 39.596 m/s

2) Please find attached the velocity graph for the vertical and horizontal velocities of the bottle and the acceleration graph for the vertical motion of the bottle, created with Microsoft Excel

at right angles to each other