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thank you so muchQuestion Paper: https://papers.xtremepape.rs/CAIE/AS and A Level/Physics (9702)/9702_s11_qp_23.pdf
Answer 4c(i)
Since all the energy is converted to kinetic, we have
\(W=\frac{1}{2}mv^{2}\)
\(0.81=\frac{1}{2}mv^{2}\)
\(v=8.05ms^{-1}\)
Answer 4c(ii)
\(\text{speed }v_{2}=8.05\times2=16.1ms^{-1}\)
Therefore, \(W=3.24J\)
Now for compression, we can use
\(W=\frac{1}{2}kx^{2}\)
and with W=3.24J, we get \(x=72mm\)
Answer 4c(iii)
At maximum height. all KE would be converted to GPE, so
\(\frac{\frac{1}{2}k{x_{1}}^{2}}{\frac{1}{2}k{x_{2}}^{2}}=\frac{36^{2}}{72^{2}}=\frac{1}{4}\)
Hope this helps!