Q. Please sketch the kinetic energy vs. height of a projectile is:-

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valentin68 eNotes educator| Certified Educator

The law of energy conservation states that the total energy of any body is the same regardless its state of movement or its position is space. This means that for a projectile that is launched from the ground (altitude 0 m) the sum of kinetic and potential energies is the same.

 `Ek +Ep = constant`

or written in terms of projectile speed and height

`m*v^2/2 + m*g*h = constant`

where the value of the constant can be determined by knowing that at Hmax there is only potential energy and at H=0 (where V= V0) there is only kinetic energy

`constant = m*g*Hmax = m*g*V_(0)^2/2`

Now we can see the dependence of kinetic energy on height h

`Ek = constant - m*g*h = m*g*(Hmax-h)`

Therefore Ek has a linear dependence on h. See figure below for its graph.

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