Physics - Center of Mass Question with Solution | TestHub

Initially, both the man and the ball are at rest, so the total momentum of the system is zero. By the principle of conservation of linear momentum, the total momentum after throwing the ball must also be zero. Let $M=60\text{ kg}$ be the mass of the man and $m=0.5\text{ kg}$ be the mass of the ball. The ball is thrown with velocity $v_b=10\text{ m/s}$. Let the recoil velocity of the man be $v_m$. Then $0=M{v}_m+m{v}_b$. So, $0=(60\text{ kg})v_m+(0.5\text{ kg})(10\text{ m/s})$. This gives $60v_m+5=0$, so $v_m=-5/60=-1/12\text{ m/s}$. The magnitude of the recoil speed is $1/12\text{ m/s}\approx 0.083\text{ m/s}$.