How to find a percentages in kinetic energy

[Kofyebs]

Stefan throws a baseball with the speed of 140 km/ℎ. The ball goes obviously in goal, but it bounces back out of the net with a speed of 50 km/ℎ. What percentage of
the kinetic energy remaining after contact with the net?

 

[Replusz]

For ’small’ velocities E=0,5m*v*v.
percentage=100*E2/E1

 

[Kofyebs]

Please check this if I am right.
BOLL = △KE = ½ = mv²
BOLL= ½(2kg)(140km/h)² - ½(2kg)(50km/h)²
BOLL= 17,100 J
%△ = 19600 J – 2500 J = 17100 J
= 17100 J / 19600 J = 0.87
= 0.80 x 100 = 87
%△ = 87%

 

[Replusz]

That’s how much was wasted…
remaining(%)=50*50/140*140*100=12,755% (some simplifications made)
So the answer: 12,8%

 

[Kofyebs]

Thanks very Replusz.

 

[Replusz]

Okay :)

 

[nasu]

To get energy in Joules the speeds have to be in m/s.
Your KE values are all wrong. Or at least in the wrong units.

The percentage does not depend on the units though.
Still your value does not look right. If the speed is halved the KE is 1/4 of the initial value.

 

[Replusz]

Yes, I know that, but we only wanted to know the percentage! Thats why I didn’t care about the conversion…
And the speed is not halfed…

 

[Kofyebs]

To get energy in Joules the speeds have to be in m/s.
Your KE values are all wrong. Or at least in the wrong units.

The percentage does not depend on the units though.
Still your value does not look right. If the speed is halved the KE is 1/4 of the initial value.

Can you please show me the right equation then.
Thanks

 

[Replusz]

The answer is correct! (I think)

 

[nasu]

Sorry, my bad. I read initial speed as 100 km/h.
Yes, the answer is correct.

However I think is important to point the wrong use of units, even if the final answer is ok.
It is already too often that students think that throw in some numbers without any justification is enough to call a problem "solved". :)