### Video Transcript

A man of mass 62 kilograms stands
at rest on an icy surface that has negligible friction. He throws a ball of mass 670 grams,
giving the ball a horizontal velocity of 8.2 meters per second. What horizontal velocity does the
man have after throwing the ball?

We can label this horizontal
velocity of the man ๐ฃ sub ๐ and start off by drawing a sketch of the
situation. In this situation, initially, we
have a man holding a ball and standing at rest on a frictionless surface. The man then throws the ball,
moving in what weโll call the positive direction with the speed ๐ฃ sub ๐ of 8.2
meters per second. Because momentum is conserved, we
know that as a result of throwing the ball, the man himself will move to the left
with some velocity weโve called ๐ฃ sub ๐. Letโs use this conservation
principle, that initial momentum is equal to final momentum, to solve for ๐ฃ sub
๐.

As we consider the initial
condition of our system, since the man and the ball are both at rest, that means
their speed is zero and, therefore, the overall initial momentum of our system is
also zero. When we consider the final momentum
of our system, after the ball has been thrown, thatโs equal to the manโs mass times
his velocity plus the ballโs mass times its velocity. Because linear momentum is
conserved, we can equate our initial and final momentum and write that zero is equal
to ๐ sub ๐๐ฃ sub ๐ plus ๐ sub ๐๐ฃ sub ๐.

We want to solve for the manโs
velocity ๐ฃ sub ๐. And thatโs equal to negative ๐ sub
๐๐ฃ sub ๐ over ๐ sub ๐. We know the mass of the man and the
ball as well as the velocity of the ball. So, weโre ready to plug in and
solve for ๐ฃ sub ๐. When we do, weโre careful to
convert the mass of the ball into units of kilograms to agree with the units of the
manโs mass. When we calculate this value, we
find itโs equal to negative 0.089 meters per second. Thatโs the velocity of the man
sliding across the ice after he has thrown the ball.