When you throw an object into the air, is the initial velocity the same as the velocity just before it hits the ground? If so, why?
Asked by: Robin Pleshek
Answer
First, let's assume you are not taking air resistance
into consideration. This is a reasonable assumption
because it's obvious that a parachute's velocity just
before it hits depends on factors other than just
gravity or drop height. Adjusting its size can influence
its speed at impact.
Without air friction, an object WILL regain its original
upward velocity just before it hits the ground on the
way down. The initial velocity on the ground represents
KINETIC ENERGY, and the initial height of 0 represents NO
POTENTIAL ENERGY. As the object rises, its kinetic
energy is gradually converted into potential energy until
at its highest point all the original kinetic energy (now
zero) has been converted into potential energy. At any
point in its travel, TOTAL kinetic and potential energy
remains constant.
The process is reversed when the object falls. Starting
at maximum potential energy (determined by its maximum
height) and zero kinetic energy (not moving), the potential
energy gradually gets converted back into kinetic energy
until just before it hits the ground. Then, potential
energy is zero and it has all the kinetic energy it had
at the start.
So the CONSERVATION OF ENERGY is why the two velocities
are the same.
Answered by: Paul Walorski, B.A. Physics, Part-time Physics Instructor
'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'