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A $1500-\mathrm{kg}$ blue convertible is traveling south, and a $2000-\mathrm{kg}$ red SUV is traveling west. If the total momentum of the system consisting of the two cars is 8000 $\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ directed at $60.0^{\circ}$ west of south, what is the speed of each vehicle?

$3.46 \mathrm{m} / \mathrm{s}$

$2.67 \mathrm{m} / \mathrm{s}$

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Rutgers, The State University of New Jersey

Numerade Educator

Simon Fraser University

University of Sheffield

Hello students. In this problem, we have given Ah, 1500 kg blue convertible off mass 1500 kg is moving towards west. Sorry south. So this is the velocity off this card in the west direction. We know that this is east. This is west. This is north and this is south. So blue convertible car is traveling towards south and red SUV is traveling towards west. Now we have given the mass off the last few years 2000 kg and we know that the total momentum off the system is 8000 kg meter per second. Total momentum if we talk about the magnitude, it is 8000 kg meter per second and direction is 60 degree west off south. 60 degree west off south. Now here I will consider in the East direction I kept. And in the North direction Jacob. So I will write the momentum further. Ballu Khan. Whatever. God, it will be cool toe am into velocity. And for the red SUV, it will be equal Toe my ass off. That s U V into velocity off this SUV. Never we have given the total momentum is a cold or okay, This now If we write the total momentum in terms off Vector, we will. Right the direction off. Total momentum is 60 degree vest off south. That means this angle has given 60 degree and this is magnitude. So if we we will write in this total momentum in vector form, we will. Right. Model P in tow. Cost 60 minus. Jacob. Okay. Plus model P Science 60 minus icon. Now, if we right the momentum off the blue convertible, it will be called mass off car into velocity in the direction in the south. So we will learn minus jacket. And now for the red SUV, the direction is in the West, so I write minus I get now, we will compared the equation we can write. This terms is equal to this term. So the light mass off below convertible into speed. So we called to more off P into core 16. So the speed off the luke and what will will be equal to 8000 in tow. Course 60. Divided by mass off blue convertible. They just 1500. If we solve this, we get the speed off. Blue convertible is equal to two point 67 Meet up 1st. 2nd that. No, again, If you talk about the red SUV, so this will be equal to this. We can write. Okay? Yeah. Science 16 from here. The spirit off there as you will be equal to 8000. Apparently 2000 into science 16. So this will be equal to around 3.46 m per second. So the speed off really should be is 3.46 And the speed off the blue convertible is 2.6 sevens and meet up a second. I hope I answered your question. Thank you.