Problem

A gun shoots a shell into the air with an initial…

02:48

Problem 55 Hard Difficulty

A firefighting crew uses a water cannon that shoots water at 25.0 $\mathrm{m} / \mathrm{s}$ at a fixed angle of $53.0^{\circ}$ above the horizontal. The firefighters want to direct the water at a blaze that is 10.0 $\mathrm{m}$ above ground level. How far from the building should they position their cannon? There are two possibilities; can you get them both? (Hint: Start with a sketch showing the trajectory of the water.)

Answer

$x=8.7 \mathrm{m}$
$x=52.5 \mathrm{m}$

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Physics 101 Mechanics

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Christina K.

Rutgers, The State University of New Jersey

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Video Transcript

So let's use the coordinates with bless y to be a poor on a less extra bit towards the light. Now, once the water leaves the cannon, it is in free fall and has an acceleration in white election Toby acceleration due to gravity, the negative sign is because, uh ah, gravity points downwards on. We have taken the positive by direction to be apart. So gravity points and negative I tid ex tenants should have a negative sight find there is no acceleration in the horizontal direction. So ecstasy, Joe. Now the components off the velocity ofthe water be not X, which is be not times goes. I know not. And this is equal to 15. Meet up once again. Similarly component off the initial velocity in my direction as we not times sign off cannot. And this is equal to 20 meters per second. Now let's use the ah, um what legal motion to find that time that gives why minus why not equal to 10 meter Andi used us to find time. So the kind of a big question with suits No, to find this perimeter is this one because we have all the parameters that we need to solve 14. Now this is equal and drinking made up a second time. Steve Bless half off negative. 9.8. I need a purse against Greg and St Script. This's equal toe. That's simplified. So this is a good 4.9 meters per seconds squared B square minus 20. Meet up for a second dynasty class. Stand me does. We can't tell Ciro now. This is a quadratic formula that gives they will be equal to to point 04 less minus one point for five seconds on DH. This gives me equal dough. I see your point for nine seconds for the minus sign on DH equal to 3.49 seconds for the last time. Now, both of these answers I physical so far P equals to 0.59 seconds. X minus X not mystical toe. We not expressed e unless there is an acceleration Dom like here. But that is just that just goes to zero because excessive. And this gives x minus x not Toby 8.8 meters. But I think wants to she pined for nine seconds. X minus X not is so Let's call it the 12 one. Does this values 52.4 meter? Let's call this to be next. Now let me explain why boot off his answers make sense. So when the camera is 8.8 meter from the building, the water hits this sport on the wall on its way up to its maximum height. Now, when the cannon is 52.4 meters from the building, it hits this sport after it has passed through its maximum height.

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