Question

2) A person with mass 65 kg, standing still, throws an object at 4m/s. If the
recoil velocity of the person is 3.5 m/s, what is the mass of the object?
Assume the surface to be frictionless.

Answer 1

The mass of the object is 56.9 kg

Explanation:

We can solve the problem by applying the law of conservation of momentum: in fact, the total momentum of the person-object system must be conserved before and after the person throws the object.

At the beginning, both are at rest, so the total momentum is zero:

$p_i = 0$

After the person throws the object, the total momentum is

$p_f = mv+MV$

where

m is the mass of the object

v = 4 m/s is the velocity of the object

M = 65 kg is the mass of the person

V = -3.5 m/s is the recoil velocity of the person

Since momentum is conserved,

$p_i = p_f\\0=mv+MV$

And solving for the mass,

$m=-\frac{MV}{v}=-\frac{(65)(-3.5)}{4}=56.9 kg$

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