How Do You Calculate the Kinetic Energy of a Moving Body?

[kaspis245]

Homework Statement

A body, which has mass of m = 1 kg , is dropped with a horizontal speed of v_o = 20 m/s . What is its kinetic energy after 4 s ?

Homework Equations

E_k = mv²/2
s = v_ot + gt²/2

The Attempt at a Solution

Is it correct?

P. S. There is a mistake: E_k = 3200 J

 

[NTW]

It's wrong. First of all, you should add the velocities as vectors. And, in this case, those vectors are at 90º...

 

[Maged Saeed]

after 4 seconds ,,
It would have a vertical component of velocity equal to (v0-gt)"which is what you have calculated in your derivative , which is incomplete too , " and a horizontal component equal to (v0 cos [theta=0])(which you haven't included)

Just find the magnitude of them and substitute the value of velocity in the kinetic energy formula

 

[kaspis245]

OK, from your answers I understood that:

v_y = v_oy - gt
So, after 4 s :
v_y = 0 - 10 m/s² * 4s = -40 m/s

v_x = 20 m/s (since it does not change)

v² = (v_y)²+(v_x)² = 2000 m²/s²

v = 45 m/s

E_k = mv²/2 = 1000 J

Corrected

 

[NTW]

You have forgotten g...

 

[kaspis245]

What about now?

 

[NTW]

What about now?

Now it's right...