Calculating Speed from a Falling Ball's Gravitational Energy

[Senjai]

Homework Statement

How far would a 1.00 Kg ball have to fall freely to reach a speed of 100 Km/h ?

Homework Equations

$$\Delta E_g = \Delta E_k$$

The Attempt at a Solution

$$\Delta E_g = \Delta E_k$$

i then expanded to:

$$mgh' - mgh = \frac{1}{2}m(v')^2 - \frac{1}{2}mv^2$$

i got rid of the 1/2's and the mass

and 0'd out the equatiosthat would equal zero…

$$2gh' = -(v')^2$$
$$h' = \frac{-(v')^2}{2g}$$

subbed in the variables and ot 5.1 x 10^2 J.. which is wrong..

appreciate any help... thanks.

 

[Sourabh N]

you got height in terms of Joules?

 

[Senjai]

the answer i got was 5.1 x 10^2 Joules, if that's what your asking...

 

[Sourabh N]

Joules is the unit of work, not height (the answer you have to calculate in #1 is height). Even if you talking about the energy content of the ball, its not 5.1 x 10^2 J.

 

[Senjai]

sorry i meant meters, I am actually not sure if its is meters... m/s / N/kg?

anyways, so let's go with meters. stil can't solve the answer..

 

[Sourabh N]

still I don't understand why you are not getting the answer. You have the equation with you, just plugin the values in your last equation and get the answer (I got 39.4 m)

 

[Senjai]

howd you get that? i still get 510...

 

[Senjai]

using

$$h' = \frac{-(v')^2}{2g}$$

 

[Sourabh N]

Check your units... you plugged in v as 100 kph and g as 9.8 m/s$$^{2}$$

 

[Senjai]

oh shii, unit conversion... sorry...