how do i calculate velocity of a falling object?

Question

Hi, i'm doing a physics project and i need to know how to calculate velocity of a falling object.

The question reads: using conservation of energy, calculate the velocity of a 2kg mass will strike the ground if it is raised 4 meters and then dropped.

can you at least provide the correct equation for this calculation.

Even if you dont know the units in meters, can you please provide the correct equation for this calculation.

thanks

Answer 1

mechanical energy (ME) = Kinetic energy + potential energy

Mechanical energy for a free falling body is the same at any instant during falling

When you leave a body to fall freely the potential energy is converted to kinetic energy.
m=2 kg
y= 4 m
g = 9.8 m/s^2

(1) >>> JUST AFTER LEAVING THE BODY. (KE=0)
(2) >>> JUST BEFORE HITTING THE GROUND. (PE=0)

ME(1) = ME(2)
KE(1) + PE(1) = KE(2) + PE(2)
0 + mgy = 1/2 mv^2 + 0
2*9.8*4= 1/2*2*v^2
v^2= 78.4
v=8.85 m/s

Answer 2

First, can you neglect air resistance???

If yes, then the answer is as follows (choose whichever units you prefer.. but remember, mass is NOT in pounds!!!!!!)

Without friction (air resistance), we have no non-conservative forces acting, and so the initial energy = final energy.

Ei = Ef

Initially, there is no KE since the object is not moving. Finally, there is no PE since the object is at ground level.. So..

PEi = KEf

mg hi = ½m vf²

g hi = ½ vf²

vf = sqrt(2g hi)



Now, if we aren't neglecting air resistance...

Air resistance is a non-conservative force; hence, it takes energy out of the system, and the speed calculated earlier will be slightly less than the speed calculated above.

Air resistance falls into a few categories: linear and quadratic. There is no closed equation for the linear form, but the quadratic form has a closed form.

To find it, we'd need to solve a differential equation (not difficult). I coudn't find it on the net and I'm too lazy to resolve for it right now. If the height's only 4 m, just ignore air resistance :)

Answer 3

Use the formula: 2da = s² or s= sqrt(2da) where
s = speed
d = distance (4 meters in your case)
a = acceleration (gravity in your case, 9.8m/sec² )
sqrt = square root

Answer 4

i'm not quite sure, but would it help if you use the equation dt/dv?