Caution! Slippery Surface!

When you collide with the other person, we know that momentum is conserved. We can therefore equate the momenta before and after that collision:

$p_{you, before} + p_{them, before} = p_{you, after} + p_{them, after}$

We know their velocity before, so we can substitute

$p_{them, before} = m_{them} v_{them, before} = m_{them} (5~\rm m/s)$ .

We also know that both velocities are zero after the collision, so the momenta are also zero afterwards:

$p_{you, before} + m_{them} (5~\rm m/s) = 0$

All that stands between us and knowing their mass is finding your momentum before the collision. Luckily, we know how much force was applied and for how long to give you that momentum. Since you started with zero momentum, the impulse ( $\Delta p$ ) is equal to your momentum before the collision ( $p_{you,before}$ ). We can calculate the impulse like so:

$\Delta p = F \Delta t$

$\Delta p = 150 ~\rm N \cdot 1.2~\rm s$

$\Delta p = 180 ~\rm kg \cdot m/s = p_{you,before}$

Substituting this into our conservation equation, we get

$180 ~\rm kg \cdot m/s + m_{them} (5~\rm m/s) = 0$

Solving for m,

$m = 36 ~\rm kg$

Interesting note - the solution is independent of your mass!

The Impulse gave to you was:

$J=F\cdot \Delta t$

$J=150\cdot 1.2$

$J=180 Ns$

Finding your acceleration after it:

$F=m\cdot a$

$150=60\cdot a$

$a=2.5 {m/s}^{2}$

Calculating your velocity after the impulse:

$v_f=v_i+at$

$v_f=0+2.5\cdot1.2$

$v_f=3 m/s$

Using the the principle of conservation of momentum:

Be $m$ the mass of the other person:

$q_f=q_i$

$60\cdot3+(-5)m=60\cdot0+0m$

$180-5m=0$

$m=180\div5$

$m=36$

Thus the other person have a mass of 36 Kilograms.

By Newton's Third Law, every action force has an equal and opposite reaction force.

Similarly, impulses that colliding objects exert on each other are equal and opposite.

Your impulse on the person $J=F\Delta t=180Ns$ , therefore their impulse on you = $-180Ns$ .

Their velocity $v=-5m/s$ (note the negative, because they are going in the opposite direction as you are).

Therefore, their mass $m = \frac{\Delta p}{v} = \frac{-180Ns}{5m/s} = 36kg$ .