"The monkey and the hunter" is a physics demonstration often used to illustrate the effect of

gravity In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the stro ...

projectile motion Projectile motion is a form of motion experienced by an object or particle (a projectile) that is projected in a gravitational field, such as from Earth's surface, and moves along a curved path under the action of gravity only. In the particul ...

. No live monkey is used in the demonstrations. The essentials of the problem are stated in many introductory guides to

physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which r ...

. In essence, the problem is as follows: A hunter with a

blowgun A blowgun (also called a blowpipe or blow tube) is a simple ranged weapon consisting of a long narrow tube for shooting light projectiles such as darts. It operates by having the projectile placed inside the pipe and using the force created by ...

goes out in the woods to hunt for monkeys and sees one hanging in a tree. The monkey releases its grip the instant the hunter fires his blowgun. Where should the hunter aim in order to hit the monkey?

Discussion

To answer this question, recall that according to

Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

's law, all objects fall with the same constant

acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

of gravity (about 9.8 metres per second per second near the Earth's surface), regardless of the object's weight. Furthermore, horizontal motions and vertical motions are independent: gravity acts only upon an object's vertical

velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...

, not upon its velocity in the horizontal direction. The hunter's dart, therefore, falls with the same acceleration as the monkey. Assume for the moment that gravity was not at work. In that case, the dart would proceed in a straight-line trajectory at a constant speed (

Newton's first law Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion ...

). Gravity causes the dart to fall away from this straight-line path, making a trajectory that is in fact a

parabola In mathematics, a parabola is a plane curve which is mirror-symmetrical and is approximately U-shaped. It fits several superficially different mathematical descriptions, which can all be proved to define exactly the same curves. One descript ...

. Now, consider what happens if the hunter aims directly at the monkey, and the monkey releases his grip the instant the hunter fires. Because the force of gravity accelerates the dart and the monkey equally, they fall the same distance in the same time: the monkey falls from the tree branch, and the dart falls ''the same distance'' from the straight-line path it would have taken in the absence of gravity. Therefore, ''the dart will always hit the monkey,'' no matter the initial speed of the dart, no matter the acceleration of gravity. Another way of looking at the problem is by a transformation of the

reference frame In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin (mathematics), origin, orientation (geometry), orientation, and scale (geometry), scale are specified by a set of reference point ...

. Earlier the problem was stated in a reference frame in which the Earth is motionless. However, for very small distances on the surface of Earth the acceleration due to gravity can be considered constant to good approximation. Therefore, the same acceleration acts upon both the dart and the monkey throughout the fall. Transform the reference frame to one that is accelerated ''upward'' by the amount with respect to the Earth's reference frame (which is to say the acceleration of the new frame with respect to the Earth is ). Because of

Galilean equivalence In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...

, the (approximately) constant gravitational field (approximately) disappears, leaving us with only the horizontal velocity of both the dart and the monkey. In this reference frame the hunter should aim straight at the monkey, since the monkey is stationary. Since angles are invariant under transformations of reference frames, transforming back to the Earth's reference frame the result is still that the hunter should aim straight at the monkey. While this approach has the advantage of making the results intuitively obvious, it suffers from the slight logical blemish that the laws of classical mechanics are not postulated within the theory to be invariant under transformations to non-inertial (accelerated) reference frames (see also

principle of relativity In physics, the principle of relativity is the requirement that the equations describing the laws of physics have the same form in all admissible frames of reference. For example, in the framework of special relativity the Maxwell equations have ...

References

External links

* An intuitive explanation: http://BrainExperiments.com/MonkeyAndHunter.aspx * A game: https://www.timetocode.org/?4e.monkeyhunt {{DEFAULTSORT:Monkey and the Hunter, The Physics experiments Thought experiments in physics Kinematics