Newton's First Law of Motion
In order to successfully perform certain types of leaps, the dancer must possess strength, technique, timing and concentration. The technicalities such as keeping your head raised, applying force to the floor with a flexed foot, and placement of the arms aid in the completion of a leap that adheres to the principles of physics.
In simpler terms, Newtons First Law of Motion states that an object at rest will remain motionless and an object in motion will continue to be in motion unless another force acts upon it. This laws pertains to general movements in dance, as well as leaping. The three main forces that act on a dancer are gravity, the normal force of the floor, and the force of friction. However, when a dancer leaps, more complex relationships to physics can be applied.
At the start of the leap, the dancer is motionless. When the dancer is ready to perform a leap, (a grand jete for example) he or she has to apply a force to the floor in order to accelerate upwards. A dancer may do this by first bending their knees (also known as plieing) and then shift their weight from one foot to another as he or she applies the force to the ground. The amount of force applied to the floor will determine the dancer's maximum height because the force applied to the floor by the dancer is equal to the force applied to the dancer by the floor (Newton's Third Law). Once the dancer is no longer in contact with the floor, their center of gravity produces a projectile motion. A projectile is the path of motion of an object based on the force of Earth. At this point, the only force acting on the dancer is the force of Earth and acceleration, in the y direction, is the only force occurring. After the dancer has reached their maximum height and velocity reaches zero, the dancer will begin to accelerate downwards until their feet return to the floor. The floor provides a force on the dancer that causes their motion to come to a rest.
Some factors that will affect a grand jete are the dancer's mass, which has a direct relationship to the gravitational force exerted downwards on the dancer and an affect on the momentum of the grand jete.
Remember that the force of earth on an object = mass * acceleration due to gravity (9.8 m/s/s) and momentum = mass * velocity.
The time in which a dancer will spend in the air depends solely on the initial upward velocity of the dancer and the angle at which he or she jumps. The following table is taken from http://www.hep.uiuc.edu/home/g-gollin/dance/dance_physics.html#8 which has recorded data to prove this principle.
height of jump time in air initial velocity
6 inches .35 seconds 5.66 ft/sec
1 foot .50 seconds 8.00 ft/sec
1 foot 6 inches .61 seconds 9.80 ft/sec
2 feet .71 seconds 11.31 ft/sec
Below is a position verses time graph of a leap. The graph represents the vertical distance of a dancer as he or she applied force to the ground, the ground exerts an equal force (Newton's Third Law) and the force of gravity is acting on the dancer as he or she is in the air.
A dancer can also create an illusion of floating during a grand jete. If the dancer is able to alter the amount of space between his or her center of gravity and the location of his or her head, this illusion can be accomplished, making the grand jete seem effortless and long.
Check out an example of a grande jete below.