Question

What is the speed of a garbage truck that is 1.60×104 kg and is initially moving at 28.0 m/s just after it hits and adheres to a trash can that is 86.0 kg and is initially at rest

Answer 1

Answer:

Assuming the mass of the garbage truck is $1.6*10^{4}$ kg, the speed of the garbage truck is $approx. = 27.8503\frac{m}{s}$.

Explanation:

This is conservation of momentum where both objects stick at the end so they have the same final velocity so our equation is:

$m_{1}v_{1initial} + m_{2}v_{2initial} = v_{both final}(m_{1} + m_{2})$

To solve for the final velocity, just divide by the sum of both masses:

$\frac{ m_{1}v_{1initial} + m_{2}v_{2initial}}{(m_{1} + m_{2})} = v_{both final}$

So, plug in the known values (remember initial velocity for the trash can is 0):

$\frac{ 1.6*10^{4}*28 + 86*0}{1.6+10^{4} + 86} = v_{both final}$