(Solved): Please help solve these physics problems with how-to steps to clarify and study (10\%) Problem 4: Yo ...

(10\%) Problem 4: You give a crate of mass $m=1.00\mathrm{kg}$ an initial speed of $v_i=4.00\mathrm{m}/\mathrm{s}$ up an incline of $?=44.7$. The crate then slides along the incline, reaches a spring of spring constant $k=75.9\mathrm{N}/\mathrm{m}$, and compresses the spring by $?s=15.0\mathrm{cm}$ before stopping. A $25\%$ Part (a) Assuming there is no friction, what is the distance, $d$, in meters, along the incline that the crate slides? $d=$ $\mathrm{m}$ $25\%$ Part (b) What distance, $d_s$, in meters, had the crate moved when it just touched the spring? $d_s=$ $\mathrm{m}$ $D$ A $25\%$ Part (c) If there were friction between the crate and incline, which of the options below woald be the correct equation for the magnitude of the kinetic friction force? $\begin{array}{l}{f}_k={?}_{k}mg\\ f_k={?}_{k}mg\cos ?\\ f_k={?}_k\cos ?\\ f_k={?}_{k}mg\mathrm{man}?\\ f_k={?}_{k}mg\sin ?\\ f_k=mg\cos ?\end{array}$ i $25\%$ Part (d) If there were friction between the crate and incline, what value of the coefficient of kinetic friction would stop the crate after it travels a distance, $d_1$, stopping just before it begins to compress the spring? ${?}_k=$ Grade Summary Dedections Poeential 1005