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Problem 52 Medium Difficulty

In a marathon race Chad is out in front, running due north at a speed of 4.00 m/s. John is 95 m behind him, running due north at a speed of 4.50 m/s. How long does it take for John to pass Chad?

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Video Transcript

so the question states that two people were running a marathon. One person is running at four meters per second while the other person that's 95 meters away is running at 4.5 meters per second. And we're trying to find when this person passes the person that's running four meters per second. So if we call this the origin say this is where the displacement is. Zero we can use our kingdom attics formulas which state that the velocity times the time, plus some initial displacement is equal to the final displacement. And so, for the person that's running at four meters per second there, velocity is for meters per second times a time with their initial displacement as 95 meters. Because we're saying the origin is where this 4.5 meter per second person is starting to run equal to the final displacement, and for this person that's running 4.5 meters per second. There. Equation, which describes their motion, is just 4.5 tee times at 4.5 times team is equal to the final um, displacement, and so when this person passes, the person that's running four meters per second, Their displacements are gonna be equal. So we can set these two equations equal to each other. And we'll get 4.5 t equals for tea plus 95. We can simplify, and we'll see that 0.5 T equals 95 and solving for tea. We get that T is equal to 190 seconds.

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John D. Cutnell, Kenneth W. Johnson

Physics

Christina Krawiec

Farnaz Mohseni

Aspen Fenzl

Meghan Miholics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Physics

Christina Krawiec

Farnaz Mohseni

Aspen Fenzl

Meghan Miholics

John D. Cutnell, Kenneth W. JohnsonPhysics

Christina Krawiec

Farnaz Mohseni

Aspen Fenzl

Meghan Miholics

John D. Cutnell, Kenneth W. Johnson

Physics