Neco 2025 Physics Question 29

A \(2.0\ \text{kg}\) block is released from rest at the top of a smooth incline \(5.0\ \text{m}\) long that makes an angle of \(30^{\circ}\) with the horizontal. At the bottom of the incline the block compresses a horizontal spring of spring constant \(k = 800\ \text{N m}^{-1}\) and comes to rest after compressing the spring by a distance \(x\). The block then slides onto a horizontal surface where the coefficient of kinetic friction is \(\mu_{k}=0.20\). (The friction acts during the compression of the spring.) Determine (a) the compression \(x\) of the spring in metres (to three significant figures) and (b) the maximum speed of the block during its motion in \(\text{m s}^{-1}\) (to one decimal place).