A bullet (mass: $0.05 \, \text{kg}$) is fired horizontally ($v = 200 \, \text{m/s}$) at a block (mass: $1.3 \, \text{kg}$) initially at rest on a frictionless surface. The block is attached to a spring ($k = 2500 \, \text{N/m}$). The bullet becomes embedded. Calculate:

Question

A bullet (mass: $0.05 \, \text{kg}$) is fired horizontally ($v = 200 \, \text{m/s}$) at a block (mass: $1.3 \, \text{kg}$) initially at rest on a frictionless surface. The block is attached to a spring ($k = 2500 \, \text{N/m}$). The bullet becomes embedded. Calculate:(a) The speed of the block immediately after the impact by the bullet.
, (b) The amplitude of the resulting oscillation of the block
, (c) The frequency of the resulting oscillations.
, (d) The equation of motion of the block (assuming that at $ t = 0 $, $ x = 0 $).
, (e) The period of the oscillation.
:

Rachel · Accepted Answer

$\boxed{ v_x \approx 7.41\,\text{m/s} } $
$ \boxed{ \Delta x \approx 0.172\,\text{m} } $
$ \boxed{ f \approx 6.85\,\text{Hz} } $
$ \boxed{ x(t) = 0.172 \, \sin(43.03\,t) } $
$ \boxed{ T \approx 0.146\,\text{s} } $

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