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Jack (mass 55.0 kg) is sliding due east with speed 8.00 m/s on the surface of a frozen pond. He collides with Jill (mass 48.0 kg), who is initially at rest. After the collision, Jack is traveling at 5.00 m/s in a direction 34.0$^\circ$ north of east. What is Jill's velocity (magnitude and direction) after the collision? Ignore friction.

$v=(55.0 \mathrm{kg})(5.00 \mathrm{m} / \mathrm{s})\left(\sin 34.0^{\circ}\right) /\left[(48.0 \mathrm{kg})\left(\sin 36.0^{\circ}\right)=5.46 \mathrm{m} / \mathrm{s}\right.$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Section 3

Momentum Conservation and Collisions

Moment, Impulse, and Collisions

Simon Fraser University

University of Sheffield

McMaster University

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problem. 8.39. We've got Jack and Jill, who apparently haven't learned anything about safety from their infamous Hill adventure on a frozen pond where we can neglect friction, Jack is sliding to the east towards Jill, whose stationery and for this since Jack and Jill both begin with Jay's, we're going to call them and be anyway, it collides with her, and then we're told that he goes off at five meters per 2nd 34 degrees north of the east, and we want to figure out what poor Jill's velocity is its magnitude and direction. So because we can neglect the friction of the ice, this is a conservation of momentum problem. But to begin with, only Jack is moving. So it's his Mass trans his initial speed, and we'll call this direction X in this direction. And then, after they run into each other, we know that Jack is moving at his final speed for the X component. It's going to be the co sign of data. They should not forget his mass because this momentum and then Jill's momentum X component goes there. So Jack's final element of his white component uh huh, like I should have a sign. And then the white component. Jill's momentum, the live action. And so, for the sake of not trying to solve an entire vector equation all at once, we can break it into two equations. And solving those for the X and Y components of Jill's speed are the components of her velocity. Rather, we find this is going to be the ratio of his best of her mass times, the change in his speed but in the development chain, the change in the relevant component of his feet. So be it. No, sorry. It's, uh, a negative of change because you subtract the final from the initial is opposed to vice versa. Yeah, Now this works out to be four point for who? For seconds. Why component of Jill's Velocity? Same story here. So because there's nothing in the white component of Jack's initial velocity, we just go straight to it being negative, and this is going to be negative. You, too, meters per second. So the magnitude of Jill's awesome good to be the same old formula for the magnitude of actor. That has always been the case. This case is only has two components. All right, You think of it is having 1/3 which is zero because they remain on the surface of the frozen pond at all times. And so her speed is 5.4 six meters per second. And then so the tangent of her angle is going to be the white component divided by the component. And the angle then will be arc tangent of that ratio. Her angle wonder being 35.9 degrees south of these drawn here sort of intuitively. And then we saw lt's like component. So that lets us know that this should be south of the East, and hopefully, this time they will learn something about safety and not keep getting themselves into these situations.

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