Graph of Kinetic Energy v. Displacement of a Falling Object

[brendan3eb]

[solved] Graph of Kinetic Energy v. Displacement of a Falling Object

Homework Statement

Draw and label a graph with energy for the y-axis and displacement for the x-axis of the kinetic energy and potential energy of an object in free-fall that started with a horizontal speed of 30 m/s from a height of 80 m.

Homework Equations

U=mgh
k=1/2mv^2

The Attempt at a Solution

I drew a straight line with negative slope for potential energy because m and g are constants in U=mgh, so it should be a linear graph, as for kinetic energy, I am sitting on the fence on whether or not to draw a straight line or a curve The v^2 makes me want to draw a curve, however, if the the potential energy is a straight line and K = E - U, then shouldn't k be directly proportional to displacement as well?

 

[Doc Al]

The v^2 makes me want to draw a curve, however, if the the potential energy is a straight line and K = E - U, then shouldn't k be directly proportional to displacement as well?

Good thinking!

Why not use a bit of kinematics to double check? What's the relationship between v (or v^2) and displacement for a falling object?

 

[brendan3eb]

ahh..

v^2=v0^2+2a(x-x0)
but since initial velocity in the y direction is 0
v^2=-2g(x-x0)

and since -2g is a constant, v^2 is directly proportional to displacement, and thus kinetic energy is directly proportional to displacement!

Thanks Doc Al!