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Carnegie Mellon University



Problem 18 Easy Difficulty

A fireman $d=50.0 \mathrm{m}$ away from a burning building directs a stream of water from a ground-level fire hose at an angle of $\theta_{i}=30.0^{\circ}$ above the horizontal as shown in Figure $P 3.18$ . If the speed of the stream as it leaves the hose is $v_{i}=40.0 \mathrm{m} / \mathrm{s},$ at what height will the stream of water strike the building?


$h = 18.71 \mathrm { m }$


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Omar B.

March 1, 2021

How long does it take an automobile traveling in the left lane of a highway at 60.0 km/h to overtake (become even with) another car that is traveling in the right lane at 40.0 km/h when the cars’ front bumpers are initially 100 m apart?

Video Transcript

So we know that the ex initial his equaling v initial co sign of Fada and we know that then the change, the displacement in the extraction is the initial co sign a fate at times t where we consult for tea. This would be equaling Delta X divided by the initial coastline of data. This is gonna be equaling 50.0 meters, divided by 40.0 meters per second times co sign of 30 degrees and this is equally 1.44 seconds. At this point, we can say that then Delta, Why equaling V? Why initial t plus 1/2 G g t squared. And here we're going to say that Delta y we're gonna choose upwards to be positive. So we have. This would be equal to the initial sign of fada Times t plus 1/2 g t squared and we can solve. This would be equally 40 0.0 meters per second sign of the 30 degrees, uh, well supplied by t of 1.44 seconds plus 1/2 times negative 9.80 meters per second squared multiplied by 1.44 seconds. Quantity squared and we find that delta Y is equaling 18.6 meters. This would be the vertical height of the street of the steaming of water in order to, uh, this would be the vertical height of the stream of water in order to hit the building. So delta Y 18.6 meters. That is the end of the solution. Thank you for watching.

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