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In a volcanic eruption, a 2400 -kg boulder is thrown vertically upward into the air. At its highest point, it suddenly explodes (due to trapped gases) into two fragments, one being three times the mass of the other. The lighter fragment starts out with only horizontal velocity and lands 274 $\mathrm{m}$ directly north of the point of the explosion. Where will the other fragment land? Neglect any air resistance.

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$-91.3 \mathrm{m}$

Physics 101 Mechanics

Chapter 8

Momentum, Impulse, and Collisions

Moment, Impulse, and Collisions

Cornell University

Hope College

University of Winnipeg

McMaster University

Lectures

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

03:30

In physics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Given a force, F, applied for a time, t, the resulting change in momentum, p, is equal to the impulse, I. Impulse applied to a mass, m, is also equal to the change in the object's kinetic energy, T, as a result of the force acting on it.

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Yeah. In discussion before going further that's this steps about a concept will be used. This motion for No here according to conservation of linear momentum. That total linear momentum of and objects before that realism is equal to that. Tell some of the linear momentum of the object after the well isn't. And we can represent this by using the equation E I. E. Equals you. We yeah, is considered it as equation. But now here I is the initial in your momentum and fear it represents the final indian momentum. Now we know that the momentum of an object is defined as the product of mass of the object and velocity of the object that is P. Is equal to a multiplier. Might be. No, they just consider this as situation you No very student problem. So here in the world and the corruption of border is strong vertically of bar. In here has had the highest wine. The boulder velocity is zero. Well this means that E. I. Is equal to zero. You meet their part second. No using the situation to the border. Before that expressed explosion is given by B. I. Equals do And multiple ever be fine. Now here we substitute 2400 kg for the mosque of the border and the role the proper second for the initial velocity after boarding. Therefore we get P. I equal to 2400, multiplied by zero. So from about we get B. I. Equals to zero. Hello graham. Meet them for a second. After the explosion. The border is divided into two fragments in the ratio the ratio one. So here we assume that the mass of the lighter fragment B. M. L. And The mass of the heavier pregnant is three times of the lighted. Thank me. And we can represent this by equation and add it was Three were give lava and help. No let us consider it as equation three. But on the other hand the total mass of the border is that some of the light and have your fragment that means and is equal to and heads plus M. N. Now Long equation three We get and is equal to C. M. L. Less. Um Hell So we get em equals two all mm and no by solving the above equation the mass of the light. Different moment in terms of mass of the border is given as And help equal to one divided by four. Yeah no this app studio This value indication three. Let me go to amazon have you for the track man in terms of myself to border. Therefore we get I am at it close to see divided by four mm. Now using equation to the final momentum of the world after the explosion is equal to the sum of the momentum of the two fragments. That means we are equal to mmh We had yes M. L. Three and now here well and be a charter velocities of the lighter and have you pregnant. Now again using the equation first figure graduation between the velocities of top fragments That is E. Equal to me. Yeah. Therefore Biggest zero equal to and edge. He adds less and L. B. And no you can write this as three divided by four. I'm mighty glad by the edge. Yes one divided by four mm marty lava. We hello so yeah reducing now. Here you go. We urge it was true. Find us. We are divided by okay now after the explosion. The time for traveling the horizontal distances X minus ex north of X divided by he adds equals through X minus X. Not of has divided but we. Yeah no. Yeah from a bow we get X minus ex law that it was X minus explore of L. You might get by E. L. Market lava. The edge Now we substitute minus we are divided by three for velocity of the heaviest recommend and 2 74 m for the value of x minus X. Note of L. Therefore bigger X minus external heads. It was Who's anti war? Yeah I did buy B. L. I keep live by minus we are divided by see so from Hubble we get x minus X. North of ads. It was too -274 divided by which is equal to minus 91 13. Neither now here negative sign indicates that the direction of the heavy effect might as opposed to the direction of the light, correct me. Therefore the Heavier segment plans 91.3 m in the south my addiction.

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