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

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