Problem

$\bullet$ A hockey puck $B$ rests on frictionless…

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Problem 29 Medium Difficulty

Accident analysis. Two cars collide at an intersection. Car $A$, with a mass of $2000 \mathrm{~kg}$, is going from west to east, while car $B$, of mass $1500 \mathrm{~kg}$, is going from north to south at $15 \mathrm{~m} / \mathrm{s}$. As a result of this collision, the two cars become enmeshed and move as one afterward. In your role as an expert witness, you inspect the scene and determine that, after the collision, the enmeshed cars moved at an angle of $65^{\circ}$ south of east from the point of impact. (a) How fast were the enmeshed cars moving just after the collision? (b) How fast was car $A$ going just before the collision?

Answer

(a) $v_{2}=7.09 \mathrm{m} / \mathrm{s}$
(b) $v_{A 1}=5.25 \mathrm{m} / \mathrm{s}$

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Physics 101 Mechanics

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Video Transcript

in this question. We have two cars. Car has a mass of 2000 kilograms. Carpi has a mass of 1500 kilograms. Car is going east, but we don't know what speed Car B has. A velocity of 15 meters per second in the south direction. Um, and the angle after the two cars crashed together is 65 degrees south of east. So, um, we are defining. First of all, that south is the Y direction East is the extraction, and theta is the angle between them. So, in part, we want to find the, um, speed of the cars, Um, after the collision. So the magnitude of the velocity, they do stick together. So the way we want to do this is just using conservation of momentum in the Y direction, since we know how much momentum there was in the initial state since we have car bees velocity. So, um, in the Y direction, the mo mentum is all carried by car. Be. So the momentum is MB, times VP, um, ends due to our definitions of, um of trig functions, we know that, um, sign of data is equal to the opposite side, which is um V Why? Or um, To keep the notation of being using v two. Why over V two So, um, this, um v two, why is equal to V two Time signed data so plugging that in here we have m b vb is equal to, um m. And now we have to use the total mass of both cars. I'm a plus MB census stick together times V two sign data rearranging to sell for V two. We have B two is equal to, um be times vb over. Um a plus m b time, uh, time sign data and plugging all this into a calculator. We find that the, um that's the cars have a speed after collision of 7.1 meters per second. Now we just need to set up a similar equation inthe e x direction to get, um, the initial velocity of car A. So, um, the massive car, a times the velocity of car A. This is in the X direction now is equal to the massive car A plus the mass of Karbi times fy two. And due to our trig functions, we actually have coastline. Data is equal to V two X over V two. Um, so we have, um at the end of this equation here, v two times, co sign of data. Now we want to solve for V a, um so rearranging this equation it's just a is equal to, um, a plus MB over m a Times V two co sign of data and again plugging all of these values in like we did in the previous part of this question. A swell as's, plugging our results for V two in. We find that car a had an initial philosophy of five point to meters per second, and that's it for this question.

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