Does velocity depend on the height of an object?

Answer 1

The height of an object suspended in a uniform gravitational field gives the object an associated potential energy. This energy is described by

Potential Energy = m*g*h

where m represents the mass of the object, g represents the acceleration of the gravitational field, and h represents the height of the object relative the bottom of its trajectory.

When the object is released, it will tend to accelerate in the direction of the gravitational field, transforming its potential energy into kinetic energy. This is referred to as "free-fall." The kinetic energy can be described by

Kinetic Energy = 0.5*m*v2

where m represents the mass of the object and v represents the instantaneous velocity of the object.

During free-fall, energy is conserved so, the total energy of the system is constant and can be described as

Energytotal = Kinetic Energy + Potential Energy

E = 0.5*m*v2 + m*g*h

This is true at any instant during free-fall, so we can rewrite it to describe velocity in terms of height and we get

v = (2(E/m - g*h))1/2

To calculate the constant E, it is convenient to set the kinetic energy to zero (when velocity is zero) and the potential energy will be at its maximum. This occurs at the initial height. Here, the total energy is equal to the potential energy.

Answer 2

the kinetic energy gained must be equal to the gravitational energy lost.

0.5mv2 = mgh

0.5v2 = gh

v2 = 2gh

so the speed is affect by the square root of the height change multiplied by a constant which is the square root of twice the magnitude of the acceleration due to gravity.

Answer 3

If you are talking about the velocity of a falling object as it hits the ground, yes its velocity depends on the height from which it falls, but also on its shape shince it is falling through the air and thus has a maximum velocity it cannot exceed no matter how high it is when it starts falling.

Notice that the object's velocity could have been almost anything before it fell.

Its velocity, neither speed nor direction, before it began to fall, didn't depend on

the height of wherever it started from.

At any given height, an airplane may be moving up fast or slow, moving down

fast or slow, or not moving up or down at all. At the same height, a glider may

be moving up or down fast or slow, and a helicopter may be moving up, down,

left, or right, fast or slow, or not moving at all.

The question talks about the "height of the object". We've been working with the altitude, but not with the heights of an object. An athletic 30-year-old lady

may be 6 feet high, and she may do some skydiving on the weekend. At different

points during the exercise she may be moving faster or slower than the 20-ft-high

airplane that took her aloft for her dive. And down below, arranged around the

little rural private airport, are a number of buildings with heights ranging from

10-ft to 50-ft, and none of them has any velocity at all.

Answer 4

The velocity of an object depends on the height only if there is a change in gravitational potential energy due to the change in height. In the absence of external forces like air resistance, the velocity at different heights will be the same if the object only has kinetic energy.

Answer 5

it's because of the gravity :)