Question

The movie "the Gods Must Be crazy " begins with a pilot dropping a bottle out of an airplane. It is recovered by a surprised native below, who thinks it is a message from the gods. If the plane from which the bottle was dropped was flying at an altitude of 500.m, and the bottle lands 400.m horizontally from the inital dropping point, how fast was the plane fling when the bottle was released.? Need to know how to get the answer

Answer 1

QUESTION:

The movie "the Gods Must Be crazy" begins with a pilot dropping a bottle out of an airplane. It is recovered by a surprised native below, who thinks it is a message from the gods. If the plane from which the bottle was dropped was flying at an altitude of 500.m, and the bottle lands 400.m horizontally from the initial dropping point, how fast was the plane fling when the bottle was released.? Need to know how to get the answer

SOLUTION:

In chosen coordinate system the coordinates of the bottle are:

$$x = v _ {0} t$$ $$y = \frac {g t ^ {2}}{2}$$

Here $v_0$ is initial velocity of the bottle, and $v_0$ is the velocity of the plane.

When bottle lands $x = x_{L} = 400 \, \text{m}$ , $t = t_{L}$ , $y = h = 500 \, \text{m}$ , hence

$$x _ {L} = v _ {0} t _ {L} \Rightarrow t _ {L} = \frac {x _ {L}}{v _ {0}} \text{ and}$$ $$h = \frac {g t _ {L} ^ {2}}{2} = \frac {g}{2} \left(\frac {x _ {L}}{v _ {0}}\right) ^ {2} \Rightarrow v _ {0} = \sqrt {\frac {g \cdot x _ {L}}{2 h}} = 39.6 \, \text{m/s}$$

ANSWER:

$$v _ {0} = 39.6 \, \text{m/s}$$