Problem

A space probe with a rest mass of $8.2 \times 10^…

03:39

Problem 46 Hard Difficulty

A football player with a mass of 88 $\mathrm{kg}$ and a speed of 2.0 $\mathrm{m} / \mathrm{s}$ collides
head-on with a player from the opposing team whose mass is 120 $\mathrm{kg}$ .
The players stick together and are at rest after the collision. Find the
speed of the second player, assuming the speed of light is 3.0 $\mathrm{m} / \mathrm{s}$ .

Answer

$-1.6$ m/s

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Physics 103

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Video Transcript

we saw this question by using moment in preservation. The total momentum before the collision is because they're total momentum after the collision. Know that after the collision they stick together and not dressed for after the collision. The momentum is the cost zero because the momentum remembers proportional to p Times V. So if the is equal to zero, then the moment will cost 202 before the momentum before the collision. Waas zero already but the momentum before the collision has two contributions one from player one and another from player to true. For the first player, we have m one 31 divided by the correction factor one minus the one divided by C Square, plus the second players momentum and to the two divided by the square. Root off one miner's V two divided by C square on the course to zero. Because off the conservation of momentum, now we have to blink in the vials that were given in the problem. So em one is close to 88. The one is because two plus two meters by second letter say that, and this is divided by the square root off one minus two divided by three Because the problem tells us pose. That seat is close to three meters by second squared plus m too, which is 120 kilograms times. Me too, which is not no divided by the square root off one miners be too divided by a squared in. These is close to zero. Now we have to solve this wall problem or be true to simplify your solution. Let us call this war term you won then 120 not plus it will be minus because we too will negative note that one player is going to the right and another one is going to the left. So 120 times be true. Divided by the square root or phone miners v choose divided by the square. He's a ghost to be want. We begin my squaring both sides of the equation to get the following 120 squared virtual square divided by one minus ritual divided by see where it goes to be one squared. No, we continue by doing the following saying this term to the other side. 120 square kinds of each square is equal to be one square minus you One squared times the true divided by C squared. No, we're saying this term to the other side. So 120 square V two square into coastal Be one squared. Uh, forgot your order term. So these plus few one squared V two divided by C squared is equal to P one square. So we have we have since just this term to the side of the equation. Now we can write it as v Chu Square times 120 square plus be one squared, divided by seas where you close to be one square Then we can stand this term to the other side To get reach you squared is equals to be one squared divided by 120 squared plus be one divided by sea squared Now take the square it off both sides to get me to as being close to be one divided by the square root off 120 squared close be one divided by sea Where now we have to plug in the values that we had before Now let us remember what waas be one The one was equals two 18 kinds. True, Divided by the square root off one miners. Two words square. These is approximately 236.129 kilograms meters per second. Then the two he's equals. Two 236 0.129 divided by the square of off 120 plus 236 0.129 divided by tree square, which is approximately one 0.6 meters by second. But remember that this player is going to the left.

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