Question

@Abhisar
A spring-loaded dart gun is compressed a distance d, then fired straight up into the air. The dart reaches a maximum height of 24 m. For a second trial, the spring is compressed a distance of 0.50d. What is the maximum height of the dart in the second trial? Assume that the effect of friction and other nonconservative forces is negligible.

3.0 m
12 m
6.0 m
48 m

Answer 1

I think its 12 not sure

Answer 2

What happened about the yesterday's question ?

Answer 3

Teacher said it was 554 that's why it was relative I the air not ground

Answer 4

To the air

Answer 5

That means my answer was correct ?

Answer 6

Yep thanks

Answer 7

Alas !

Answer 8

Is it 12 because its compressed to half the length

Answer 9

one min !

Answer 10

Yes that's correct. But let me show you a mathematical way to calculate/prove it.

Answer 11

The potential energy stored in the spring while we compress it is transferred to the dart which gets converted into its kinetic energy. The maximum height attained by the dart will only be due to this energy. Now in

\(\huge\sf Case~1\)
\(\sf \huge\frac{1}{2}k.d^2=mg\times24\\~\\~\\\large k=48mg/d^2\)

Answer 12

Now, in case 2

\(\large\sf \frac{1}{2}.k.(0.5d)^2=mgh\\~\\~substitute~the~value~of~k~and~find~h\)

Answer 13

I got 12 thanks

Answer 14

\(\color{red}{\huge\bigstar}\huge\text{You're Most Welcome! }\color{red}\bigstar\)
\(~~~~~~~~~~~~~~~~~~~~~~~~~~~\color{green}{\huge\ddot\smile}\color{blue}{\huge\ddot\smile}\color{pink}{\huge\ddot\smile}\color{red}{\huge\ddot\smile}\color{yellow}{\huge\ddot\smile}\)

Answer 15

Maximum height will be 6m. This means you didn't solved it !

Answer 16

\(\color{blue}{\text{Originally Posted by}}\) @Abhisar
Now, in case 2

\(\large\sf \frac{1}{2}.k.(0.5d)^2=mgh\\~\\~substitute~the~value~of~k~and~find~h\)
\(\color{blue}{\text{End of Quote}}\)

\(\large \sf \frac{1}{2}.\frac{48mg}{d^2}\times\frac{d^2}{4}=mgh\)

So h=6m @akohl