Question

A cannon is rigidly attached to a carriage,which can move along horizontal rails but is connected to a post by a large spring, initially unstretched and with force constant $k=2.00\times {10}^{4}N/m$, as shown in Figure $P9.70$. The cannon fires a $200-kg$ projectile at a velocity of $125m/s$ directed ${45.0}^o$ above the horizontal.
Assuming that the mass of the cannon and its carriage is $5000kg$. find the recoil speed of the cannon.

Answer 1

Given,

spring constant $k=2\times {10}^{4}N/m$

velocity of ball is $V=125m/s$

mass of ball is $m=200kg$

angle of projection is ${45}^{\circ }$

mass of cannon and its carriage is $5000kg$

Here, momentum is conserve because gravity and normal force are acting in $x$ direction therefore, we can write,

$P_i=P_{f}m{v}_{i}cos45=(m+M)v_f$

Substitute all value in above equation

$200\times 125\times \frac{1}{\sqrt{2}}=5000v_f{v}_f=\frac{200\times 125}{5000\times \sqrt{2}}{v}_f=3.54m/s$

Hence, recoil speed of the cannon is $3.54m/s$