Question

A 90 kg man lying on a surface of negligible friction shoves a 63 g stone away from himself, giving it a speed of 4.4 m/s. What speed does the man acquire as a result

Answer 1

the speed acquired by the man is:
`0.00308\,\,(m)/(s)`

Step-by-step explanation:

Use conservation of linear momentum to solve this problem, and make sure you start by converting the 63 g stone mass into kilograms = 0.063 kg.

Now from conservation of linear momentum, the momentum imparted to the stone (which is the product of the stone's mass time its speed) must equal in magnitude that of the 90 kg man. Then we need to find the unknown speed of the man:

`m_1\.v_1=m_2\,v_2\\0.063\,(4.4)\,(kg\,m)/(s) =v_2\,(90\,\,kg)\\0.2772\,(kg\,m)/(s)=v_2\,(90\,\,kg)\\v_2=(0.2772)/(90) \,(m)/(s) \\v_2=0.00308\,\,(m)/(s)`

therefore the speed acquired by the man is:
`0.00308\,\,(m)/(s)`