Video: Conservation of Momentum

A man of mass 62 kg stands at rest on an icy surface that has negligible friction. He throws a ball of mass 670 g, giving the ball a horizontal velocity of 8.2 m/s. What horizontal velocity does the man have after throwing the ball?

02:09

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 ๐‘ฃ sub ๐‘š 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 weโ€™ll call the positive direction with the speed ๐‘ฃ 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 weโ€™ve called ๐‘ฃ sub ๐‘š. Letโ€™s use this conservation principle, that initial momentum is equal to final momentum, to solve for ๐‘ฃ sub ๐‘š.

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, thatโ€™s equal to the manโ€™s mass times his velocity plus the ballโ€™s 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‘š sub ๐‘š๐‘ฃ sub ๐‘š plus ๐‘š sub ๐‘๐‘ฃ sub ๐‘.

We want to solve for the manโ€™s velocity ๐‘ฃ sub ๐‘š. And thatโ€™s equal to negative ๐‘š sub ๐‘๐‘ฃ sub ๐‘ over ๐‘š sub ๐‘š. We know the mass of the man and the ball as well as the velocity of the ball. So, weโ€™re ready to plug in and solve for ๐‘ฃ sub ๐‘š. When we do, weโ€™re careful to convert the mass of the ball into units of kilograms to agree with the units of the manโ€™s mass. When we calculate this value, we find itโ€™s equal to negative 0.089 meters per second. Thatโ€™s the velocity of the man sliding across the ice after he has thrown the ball.

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