A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0

Question

A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.992 kgthat rests on a frictionless, horizontal surface and is attached to a coil spring. The impact compresses the spring 15.0 .cm Calibration of the spring shows that a force of 0.750 Nis required to compress the spring 0.250 cm .(Figure 1)

Part A

Find the magnitude of the block's velocity just after impact.

Part B

What was the initial speed of the bullet?

Figure1 >>>> https://session.masteringphysics.com/problemAsset/2039222/1/YF-08-043.jpg

Explanation / Answer

Given, 0.750 N is req for 0.25 cm compression
0.750 = k*0.25*10^-2
k = 300

a) Let block's velocity just after impact be v
0.5mv^2 = 0.5kx^2
0.5*(0.008+0.992)*v^2 = 0.5*300**(0.15)^2
v = 2.598 m/s

b) initial speed of bullet = u
0.008u = 1v
u = 324.759 m/s

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