Answer:
Assuming the mass of the garbage truck is [tex]1.6*10^{4}[/tex] kg, the speed of the garbage truck is [tex]approx. = 27.8503\frac{m}{s}[/tex].
Explanation:
This is conservation of momentum where both objects stick at the end so they have the same final velocity so our equation is:
[tex]m_{1}v_{1initial} + m_{2}v_{2initial} = v_{both final}(m_{1} + m_{2})[/tex]
To solve for the final velocity, just divide by the sum of both masses:
[tex]\frac{ m_{1}v_{1initial} + m_{2}v_{2initial}}{(m_{1} + m_{2})} = v_{both final}[/tex]
So, plug in the known values (remember initial velocity for the trash can is 0):
[tex]\frac{ 1.6*10^{4}*28 + 86*0}{1.6+10^{4} + 86} = v_{both final}[/tex]
